WO2020143927A1

WO2020143927A1 - Source for high-dimensional entangled photon pairs

Info

Publication number: WO2020143927A1
Application number: PCT/EP2019/061387
Authority: WO
Inventors: Anton Zeilinger; Mayukh LAHIRI; Armin HOCHRAINER; Mario KRENN; Jaroslav KYSELA; Manuel Erhard
Original assignee: Österreichische Akademie der Wissenschaften
Priority date: 2019-01-09
Filing date: 2019-05-03
Publication date: 2020-07-16

Abstract

The invention concerns an apparatus for producing higher-dimensionally quantum-correlated and/or entangled photon pairs, whereas the photon pairs are correlated and/or entangled in a spatial mode in dimension equal to or higher than three, whereas the apparatus comprises a pump laser to pump down-conversion crystals, a two-dimension-module with two down-conversion crystals and a mode-shifter in order to produce two-dimensionally correlated and/or entangled photon pairs, and one or more additional-dimension-module/s, whereas each additional-dimension-module in the apparatus adds one dimension to the produced two-dimensionally correlated and/or entangled photon pairs, whereas each additional-dimension-module comprises an additional down-conversion crystal pumped by the pump laser and by the before produced down-conversion beam and an additional mode-shifter, whereas the photon pairs and the pump laser are coherent in space and time in each additional down-conversion crystal, whereas the mode-shifter of the two-dimension- module and/or each additional-dimension-module - is arranged in the pump beam before the down-conversion crystal, and/or - is arranged in the down-conversion photon pair beam after the down-conversion crystal.

Description

Source for high-dimensional entangled photon pairs

The invention concerns an apparatus for producing higher-dimensionally quantum correlated and/or entangled photon pairs, whereas the photon pairs are correlated and/or entangled in a spatial mode in dimension equal or higher than three, whereas the apparatus comprises a pump laser to pump a down-conversion crystal, and a two-dimension-module in order to produce two-dimensionally correlated and/or entangled photon pairs, whereas the apparatus further comprises one or more additional-dimension-module/s, whereas each additional-dimension-module in the apparatus adds one dimension to the produced two-dimensionally correlated and/or entangled photon pairs and a method to provide higher-dimensionally quantum correlated and/or entangled photon pairs, whereas the photon pairs are correlated and/or entangled in a spatial mode in dimension equal or higher than three, whereas the method comprises the steps of providing two-dimensionally correlated and/or entangled photon pairs by a two-dimension-module comprising at least one down- conversion crystal pumped by a pump beam of a pump laser and a mode-shifter, and adding one or more dimension to the two-dimensionally quantum correlated and/or entangled photon pairs..

Entangled photon sources for two-dimensional states are for example known from US 6 424665 B1. Sources like this cannot be used to produce higher-dimensionally quantum correlated and/or entangled photon pairs.

An objective of the present invention is to provide an improved apparatus for producing higher-dimensionally quantum correlated and/or entangled photon pairs and an improved method to provide higher-dimensionally quantum correlated and/or entangled photon pairs.

This object is achieved by an apparatus for producing higher-dimensionally quantum correlated and/or entangled photon pairs of claim 1 , whereas the photon pairs are correlated and/or entangled in a spatial mode in dimension equal or higher than three, whereas the apparatus comprises a pump laser to pump a down -conversion crystal and a two-dimension-module with at least one down-conversion crystal pumped by the pump laser and a mode-shifter in order to produce two-dimensionally correlated and/or entangled photon pairs, whereas the apparatus further comprises one or more additional-dimension-module/s, whereas each additional-dimension- module in the apparatus adds one dimension to the produced two-dimensionally correlated and/or entangled photon pairs, whereas each additional-dimension- module comprises an additional down-conversion crystal pumped by the pump laser and by the before produced two-dimensional beam, and an additional mode-shifter, whereas the two-dimensionally correlated and/or entangled photon pairs and the pump laser are coherent in space and time in each additional down-conversion crystal, whereas the mode-shifter of the two-dimension-module and/or each additional-dimension-module

- is arranged in the pump beam before the down-conversion crystal, and/or

- is arranged in the down-conversion photon pair path after the down-conversion crystal.

The object is further achieved by a method to provide higher-dimensionally quantum correlated and/or entangled photon pairs, whereas the photon pairs are correlated and/or entangled in a spatial mode in dimension equal or higher than three according to claim 15,

whereas the method comprises the steps of

I) providing two-dimensionally correlated and/or entangled photon pairs by a two- dimension-module comprising at least one down-conversion crystal pumped by a pump beam of a pump laser and a mode-shifter,

II) add one or more dimension to the two-dimensionally quantum correlated and/or entangled photon pairs by passing the pump beam and the two-dimensionally correlated and/or entangled photon pairs through one or more additional-dimension- module/s in order to add one additional dimension to the two-dimensionally correlated and/or entangled photon pairs by each additional-dimension-module, whereas the two-dimensionally correlated and/or entangled photon pairs and the pump beam are coherent in space and time in each additional down-conversion crystal, whereas each additional-dimension-module comprises an additional down- conversion crystal pumped by the pump beam and an additional mode-shifter.

In a preferred embodiment the spatial mode can be any spatial mode family equal or higher than dimension three, provided the set of modes consists of orthogonal modes. Preferably the mode can be a Laguerre-Gaussian mode, a Hermit-Gaussian mode, an Ince-Gaussian mode, and/or a linear polarized mode. More preferably the mode can be described by Laguerre-Gaussian mode using two indices, the radial index (p) and the azimuthal index (I), whereas the photon pairs are correlated and/or entangled in one of the indexes (p) or (I) or both of the indexes (p) and (I). The azimuthal index (I) describes the orbital-angular-momentum carried by a single photon. For this a mode shifter for either of the two indices can be realized using spatial-light modulators, or a spiral phase plate, or a liquid crystal, or a sign switch comprising a mirror, or a vortex phase plate, or an q-plate.

Versatile and high-brightness sources of high-dimensionally entangled photon pairs are important for emerging quantum technologies such as secure quantum

communication. Here a scalable apparatus and method to create arbitrary high- dimensionally entangled photon pairs in orbital angular momentum or other modes are shown. The apparatus and method rely on indistinguishable photon pairs created coherently in different sources. It shows how to create two-dimensionally entangled states and demonstrate how to increase incrementally the dimensionality by one. The generated states retain their quality even in higher dimensions. In addition, the modular structure of the approach allows for generalization to various degrees of freedom and even implementation in integrated compact devices.

The transition from two- to multi-dimensionally entangled quantum systems brings about radical improvements in the distribution and processing of quantum

information. Such systems are of great importance in communication over high- capacity quantum channels, noise resistant quantum key distribution, and even experiments interesting from more fundamental perspective such as tests of local realism or a teleportation of the complete information carried by a single photon. In view of these applications, high-quality sources of multi-dimensionally entanglement are therefore highly desirable.

The apparatus and the method comprise a source of entangled photon pairs versatile as both magnitudes and phases in a quantum state which can be adjusted

completely arbitrarily. Furthermore, the implementation of the source has a modular structure. The modularity, together with the fact that adding one dimension to the entangled state increases the count rates accordingly, makes the approach scalable. High brightness of the source is ensured as all photons are produced already in the desired modes and no photons have to be discarded by post-selection.

In the following the entanglement by path identity for OAM as an example of the possible modes is explained.

Consider a simple setup consisting of two nonlinear crystals aligned in series, each emitting pairs of photons via SPDC (spontaneous parametric down conversion). The paths of the down-converted photons emitted from the first and second crystals are overlapped perfectly and pairs of photons leaving the setup are detected. In such a scenario, one observes an interference pattern in the rate of detected photon pairs. This phenomenon can be understood as an interference between two possible ways of creating the photon pair. It emerges when the two down-conversion processes are indistinguishable and not even in principle any information can be obtained as to where the detected photons were created.

The resulting quantum state of the photon pair is a coherent superposition of the two possibilities where I 0, 0 > is the state of a down-

converted photon pair. Numbers in ket vectors (I >) refer to the OAM quanta of respective photons. By altering the relative phase f between the two SPDC processes one can either enhance or completely suppress generation of down- converted pairs. Note that by setting f = 0 the rate of down -converted photons is enhanced not due to multiple photon emission, but due to an increased probability of generating a single pair. At any given time no more than one pair of photons is present in the setup as the power of the pump beam is low.

The produced quantum state changes considerably when a mode-shifter is for example inserted between the two crystals. The mode-shifter adds a quantum of OAM to each photon originating in the first crystal and thus acts as an element of distinguishability. In all other degrees of freedom, the two sources of photons remain indistinguishable and the quantum state of detected photons turns out to be a maximally entangled state

The approach can be readily generalized for higher dimensions. By adding additional crystals, mode- and phase- shifters, arbitrary high-dimensionally entangled quantum states of the form

can be created. The magnitudes of can be set by pumping each

crystal independently with properly adjusted power. The approach is not restricted to the generation of states of the form By using different

mode-shifters for either of the two photons in a down -converted pair, completely arbitrary states can be created

where and are

different OAM modes for the two down-converted photons.

The modularity of the setup and the fact that only two kinds of elements crystals, mode-shifters are needed is the strength of this approach. In addition, phase-shifters can be used the change the phase of the state. But when an apparatus or method is built for a specific state no phase-shifters is necessary. It promises high brightness, scalability in the dimension, and versatility of generated states. A very appealing feature of the method is that different families of modes can be utilized. It is therefore possible to generate high-dimensionally entangled photon pairs in specialized modes, which are optimized, for example, for free-space communication or even for fiber-based systems. Interestingly, the widely used cross-crystal scheme is the simplest example of the above approach, where two-particle states are entangled in polarization.

In the following preferred embodiments of the apparatus according to claim 1 and the method according to claim 18 are presented. In a preferred embodiment of the apparatus the photon pairs are correlated and/or entangled in orbital angular momentum (OAM) or spin angular momentum (SAM).

In a preferred embodiment of the apparatus the mode-shifter of the two-dimension- module and/or each additional-dimension-module

- is/are arranged in the pump beam before the down-conversion crystal in order to add a quantum or quanta of OAM or SAM to the pump beam, and/or

- is/are arranged in the down-conversion photon pair path after the down-conversion crystal in order to add a quantum or quanta of OAM or SAM to the down-conversion photon pairs.

In a preferred embodiment of the apparatus one, or two, or three, or four, or five or more additional-dimension-modules are arranged in the apparatus, preferably are arranged in such a way, that the down-conversion photons of the two-dimension- module passes through the down-conversion crystals of the one, or two, or three, or four, or five or more additional-dimension-module.

In a preferred embodiment of the apparatus the two-dimension module comprises a first and a second down-conversion crystal to produce coherent down -converted photon pairs.

In a preferred embodiment of the apparatus the two-dimension module comprises a Mach-Zehnder interferometer in order to separate the pump beams of the first and second down-conversion crystals, and

whereas the photon pairs of the first down-conversion crystal and the pump beam are coherent in space and time in the second down-conversion crystal.

In a preferred embodiment of the apparatus the one or each additional-dimension- module comprises at least one Mach-Zehnder interferometer in order to separate the pump beam of the additional down-conversion crystal from the pump beams of the before and/or behind arranged down-conversion crystals.

A benefit of the Mach-Zehnder configuration of the additional-dimension-module and/or the two-dimension module is that the focus parameter and the alignment of the pump beam and the down-conversion photon pairs can be adjusted separately. Also, the components, e.g. lenses, mirrors as well as the phase-shifter and mode- shifter can be optimized for the different wavelengths and can be placed either in the pump beam or the down-conversion photon pair path. In addition, the magnitude of the pump beam in each crystal can be adjusted separately. Thus, to adjust phases and magnitudes for individual modes in the quantum state independently, the pump and down-converted beams for each crystal are manipulated separately.

In a preferred embodiment of the apparatus the additional down-conversion crystal is arranged in an output arm of the Mach-Zehnder interferometer, and/or within the Mach-Zehnder interferometer of the next additional-dimension-module.

The output arm of the Mach-Zehnder interferometer can also be called output port.

In a preferred embodiment_of the apparatus the additional down-conversion crystal is arranged within the Mach-Zehnder interferometer of the additional-dimension- module.

In a preferred embodiment of the apparatus an additional laser beam is injected in the Mach-Zehnder interferometer and the interfering beams of the additional laser are monitored behind the interferometer by a photodiode in order to stabilize the Mach- Zehnder interferometer by a piezo-actuator driven mirror.

In a preferred embodiment of the apparatus the components in the two-dimension module are arranged one behind the other in a linear manner.

In a preferred embodiment the phase-shifter and/or mode shifter are/is arranged only in the pump beam or only in the down-conversion photon pair path influencing only the pump beam or the down-conversion photon pairs for each module.

In a preferred embodiment of the apparatus the crystals in the two-dimension module and the mode-shifter are arranged so, that the pump beam and the down-conversion photon pair path overlap spatially in, and behind the crystal.

In a preferred embodiment the phase-shifter and/or mode shifter are wavelength dependent components and arranged in the pump beam and/or the down-conversion photon pair path, influencing only the pump beam and the down -conversion photon pairs.

In a preferred embodiment of the apparatus the components in additional-down- conversion module are arranged one behind the other in a linear manner.

In a preferred embodiment of the apparatus the additional-down-conversion crystal and the additional-mode-shifter are arranged so, that the pump beam and the down- conversion photon pair path overlap spatially before, in, and behind the additional- down-conversion crystal.

In a preferred embodiment the apparatus comprises at least one phase shifter arranged in the pump beam before the down-conversion crystal, or in the down- conversion photon pair path behind the down-conversion crystal.

In a preferred embodiment of the apparatus the mode shifter of the two-dimension- module and/or each additional-dimension-module is a spiral phase plate, or a liquid crystal, or a sign switch comprising a mirror, or a vortex phase plate, or an q-plate, or a spatial light modulator (SLM) in order to add quanta of OAM or SAM to the pump beam photons or the down-conversion photon pairs.

In a preferred embodiment of the method the mode-shifter of the two-dimension- module and/or each additional-dimension-module

- is arranged in the pump beam before the down-conversion crystal in order to add a quantum or quanta of OAM to the pump beam, and/or

- is arranged in the down-conversion photon pair path after the down-conversion crystal in order to add a quantum or quanta of OAM or SAM to the down-conversion photons.

In a preferred embodiment of the method in step II) one, two, three, four, five or more dimensions are added by one, two, three, four, five or more additional-dimension- modules, preferably are arranged in such a way, that the down-conversion photon pairs of the two-dimension-module passes through the down-conversion crystals of each additional-dimension-module. In a preferred embodiment of the method in step I) a first and a second down- conversion crystal are provided in order to generate the two-dimensional down- converted photon pairs.

In a preferred embodiment of the method in step I) the two-dimension-module comprises a Mach-Zehnder interferometer in order to separate the pump beams of the first and second crystals, and

whereas the photon pairs of the first crystal and the pump beam are coherent in space and time in the second down-conversion crystal.

In a preferred embodiment of the method in step II) the additional-dimension-module comprises a Mach-Zehnder interferometer separate the pump beam of the additional down-conversion crystal from the pump beams of the before and/or behind arranged down-conversion crystals.

In a preferred embodiment of the method the additional down-conversion crystal is arranged and pumped in an output arm of the Mach-Zehnder interferometer, and/or in the Mach-Zehnder interferometer of the next additional-dimension-module.

In a preferred embodiment of the method the additional down-conversion crystal is arranged in the Mach-Zehnder interferometer of the additional-dimension-module.

In a preferred embodiment of the method an additional laser beam is injected in the Mach-Zehnder interferometer and the interfering beams of the additional laser are monitored behind the interferometer by a photodiode in order to stabilize the Mach- Zehnder interferometer by a piezo-actuator driven mirror or a similar optical element that is capable of manipulating the relative phase difference.

In a preferred embodiment of the method in step I) the two-dimension module comprises a first and a second down-conversion crystal in order to produce coherent down -converted photon pairs. In a preferred embodiment of the method step I) the components are arranged one behind the other in a linear manner.

In a preferred embodiment the phase-shifter and/or mode shifter are wavelength dependent components and arranged in the pump beam and the down -conversion photon pair path, influencing only the pump beam and the down -conversion photon pairs.

In a preferred embodiment of the method in step I) the two-dimension module crystals and the mode-shifter are arranged so, that the pump beam and the down- conversion beam overlap spatially in, and behind the crystals.

In a preferred embodiment of the method step II) the components are arranged one behind the other in a linear manner.

In a preferred embodiment of the method in step II) the additional-down-conversion crystal and the additional-mode-shifter are arranged so, that the pump beam and the down-conversion photon pair path overlap spatially before, in, and behind the additional-down-conversion crystal.

In a preferred embodiment of the method the apparatus comprises at least one phase shifter arranged in the pump beam before the down-conversion crystal, or in the down-conversion photon pair path behind the down-conversion crystal in order to change the phase.

In a preferred embodiment of the method the mode shifter of the two-dimension- module and/or each additional-dimension-module is a spiral phase plate, or a liquid crystal, or a sign switch comprising a mirror, or a vortex phase plate, or an q-plate, or a spatial light modulator (SLM) in order to add a quantum of OAM or SAM to the pump beam photons or the down-conversion photon pairs.

In a preferred embodiment of the method the method provides higher-dimensionally quantum correlated and/or entangled photon pairs for a communication channel between two parties. In a preferred embodiment of the method the two photons of each photon pair are

- collinear and separated by a polarizing beam splitter, or a wavelength dependent means, preferably a wavelength dependent mirror, or

- non-collinear,

in order to transmit one photon and reflect the second photon of each photon pair in order to send one photon to the first party and the second photon to the second party.

In a preferred embodiment of the method each party detects the higher-dimensionally quantum correlated and/or entangled photons in a detection module, comprising at least a spatial light modulator (SLM) and a single photon detector. In a preferably embodiment a spiral phase plate, or a liquid crystal, or a sign switch comprising a mirror, or a vortex phase plate, or an q-plate can be used. Preferably the spatial overlap of the pump beam and the down-conversion photon pair path of the two- dimension module and/or the additional dimensional module is at least in the crystal and the detector, so that the detector is not able to distinguish in which crystal the photon pair is generated.

The object is further achieved by a communication apparatus, whereas the communication apparatus comprises a communication channel between two parties, whereas the communication apparatus comprises further an apparatus according to one of the above described apparatus providing higher-dimensionally quantum correlated and/or entangled photon pairs for the communication between the parties.

In a preferred embodiment the communication apparatus comprises a polarizing beam splitter or a wavelength dependent means, preferably a wavelength dependent mirror for the separation of the two photons of each photon pair.

In a preferred embodiment the communication apparatus comprises two parties each comprising a detection module with an optical measurement means to measure the OAM or SAM or another spatial mode, preferably at least a spatial light modulator (SLM) or an interferometer, or a mach-zehnder interferometer with Dove-prism or a diffractive optics element such as multi-plane-light-conversion as optical measurement means and a single photon detector for the detection of the higher- dimensionally quantum correlated and/or entangled photons.

In the following, the invention will be explained by way of preferred embodiments illustrated in the drawings, yet without being restricted thereto. In the drawings:

Fig. 1 a: basic concept of two coherent SPDC processes to produce a two- dimensionally entangled Bell state;

Fig. 1 b: concept of Fig. 1 a with the addition of a third crystal to increase the entanglement dimension by one;

Fig. 1 c: multiple setups from Fig. 1 a to create a high-dimensionally entangled state;

Fig. 2: apparatus to produce a 3-dimensional entangled photon state;

Fig. 3: real and imaginary part of the density matrices of three three- dimensionally entangled states;

Fig. 4: comparison of coincidence-count signal fluctuations with active

interferometer stabilization and inactive interferometer stabilization;

Fig. 5: detailed setup of the apparatus to produce a 3-dimensionally entangled photon state;

Fig. 6: Interference of two SPDC processes in two crystals from Fig. 1a;

Fig. 7: real and imaginary part of the density matrices of two two-dimensionally entangled states;

Fig. 8: normalized coincidences for different projective measurements of OAM in the computational basis.

Consider a simple setup consisting of two nonlinear crystals 1 aligned in series and pumped coherently by a laser beam 4, as shown schematically in Fig. 1 a. Either crystal 1 may emit a pair of photons via SPDC (spontaneous parametric down- conversion). The propagation paths of down-converted photons 2 coming from the two crystals 1 are over-lapped perfectly so that once detected by detection means 3 the photon pair cannot be traced back to either the first or the second crystal 1. The pump beam 4 for both crystals possesses zero quanta of optical angular momentum, in the following called OAM. Nevertheless, the photons originating in the first crystal 1 acquire a quantum of OAM by propagating through mode-shifters 5. As the two down-conversion processes are (apart from the OAM) indistinguishable, the resulting state of detected photons turns out to be a coherent superposition

when I 0, 0 > is the state of a down -converted photon pair and f is the phase between the two SPDC processes imparted by a phase-shifter 6. The phase-shifter 6 is not necessary in this setup, leading to a fixed state without the phase-shifter 6. Numbers in ket vectors refer to the OAM quanta of respective photons.

Please note, Fig. 1 are schematically representations for better illustration. In a concrete setup the pump laser beam 4 and the down-converted photons 2 overlap spatially in the crystals 1. The propagation paths of the down-converted photons and the laser beam are identical, differing only in wavelength, diffraction, and so on, according to the Gaussian pump beam and the focus in the crystals. Also, the mode- shifter 5 and phase shifter 6 are shown only schematically. In a real setup the mode- shifter 5 and phase shifter 6 can be placed only in the path of the down-converted photons or only in the laser beam, or the mode-shifter 5 and phase shifter 6 can be wavelength-dependent to influence either the down-converted photons or the laser beam.

The number of utilized crystals 1 , phase- 6 and mode-shifters 5 can be increased, see Fig. 1 b, and Fig. 1c, to generate high-dimensionally entangled states of the form

where d is the state dimension and c_m are complex amplitudes. The magnitudes of c_m can be set by pumping each crystal independently with properly adjusted power. By using different mode-shifters 5 for either of the two photons in a down -converted pair, completely arbitrary states can be created

where r_m and s_m are different OAM modes for the two down-converted photons. FIG. 1 a shows the basic concept. As the two coherent SPDC processes are indistinguishable the photon pairs are produced in a two-dimensionally entangled Bell state The quantum of OAM is delivered to the photon

by a phase-shifter 5, preferably a spiral phase plate. Fig. 1 b shows the addition of the third crystal 1 to the setup increases the entanglement dimension by one. One can stack multiple setups from Fig. 1 a to create a high-dimensionally entangled state

as shown in Fig. 1 c in arbitrary dimension d,

where relative phases can be adjusted by appropriate choice of phase-

shifters <pj. The magnitudes of individual modes can also be modified by varying the power with which respective crystals are pumped.

The setup of the approach described above is based on the scheme in Fig. 1 with two modifications. First, as we want to adjust phases and magnitudes for individual modes in the quantum state independently, the pump and down -converted beams for each crystal 1 are manipulated separately.

Therefore, two Mach Zehnder interferometers are used in the setup as shown in Fig. 2. The two Mach Zehnder interferometers in Fig. 2 are sharing a polarizing beam splitter and a mirror. An alternative approach with no need for beam separation would be to use wavelength-dependent optical elements as we discuss below. Second, for technical reasons the down-converted photon pairs were not emitted in a perfectly collinear manner. This has detrimental effects on the operation of the mode-shifter 5. It is solved here by placing the mode- shifter 5 into the pump beam 4. The mode shifter 5 can also be placed in the down-conversion beam 2.

The two-dimensionally entangled states are produced by the setup shown in Fig. 2 in box 2 dim with two crystals 1 , which are pumped by separate beams 4. The Mach- Zehnder interferometers are built by two polarizing beam-splitter 8 and two dichroic mirrors 16. The first Mach-Zehnder interferometer consists of two polarizing beam splitter 8 two dichroic mirrors 16, whereas each further Mach-Zehnder interferometer consists of additional one polarizing beam-splitter 8 and one dichroic mirror 16 and using one of the beam splitter 8 and one of the dichroic mirror 16 of the before arranged Mach-Zehnder interferometer. The pump beam 4 is separated for each crystal 1. The dichroic mirrors 16 reflect the pump beam of the before placed crystal 1 , so only the separate pump beam, also reflected on the dichroic mirrors 16 traveling from the bottom of Fig. 2 to the top, can pump the next crystal 1. The pump beam 4 for the first crystal 1 on the left side in box 2 dim possesses zero quanta of OAM and so do the down-converted photons of the first crystal 1 .

The pump beam for the second crystal 1 , on the right side of the box 2 dim acquires as an example here four quanta of OAM due to the mode-shifter 5, preferably spiral phase plate (SPP), which is inserted into the beam 4. Consequently, each down- converted photon generated in the second crystal 1 carries two quanta of OAM. To increase the entanglement dimensionality, we add an additional third crystal 1 , in box +1 dim in Fig. 2. An extra mirror (not shown in Fig. 2) in the pump beam 4 for the third crystal 1 inverts the sign of the OAM value of the pump 4 and acts as a mode- shifter 5. As a result, the third crystal 1 produces photons in the state I - 2, -2 >. Incorporating the third crystal 1 thus leads to an increase in the state dimensionality from two to three dimensions. The resulting quantum state reads:

Magnitudes a, b and g of the entangled state can be changed by adjusting the relative pump power for each crystal 1. This will be explained in Fig. 5. The relative phases and

are set by positioning a trombone system (not shown in Fig. 2) that acts as a phase-shifter.

The box +1 uses the PBS and the dicrotic mirror of the box 2 dim to that only the additional components of the PBS 8 on the bottom right side, or a mirror and the dichroic mirrors 16 on the upper right side together with the right crystal 1 is needed. Preferably each additional dimension module comprises only a PBS 8, and a dichroic mirror 16 and a crystal and uses two components of the before installed module.

We use type II SPDC for all three crystals 1 for example with ppKTP crystal

(periodically poled KTP). Type II means that the down-converted photons possess a different polarization. In a Type I configuration (for example with two KDP crystals) the photons of each pair possess the same polarization. In order to measure the entangled state, we first deterministically separate the two down -converted photons by a polarizing beam splitter 8. Two spatial light modulators (SML) 9 in combination with single mode fibers are used to perform any projective measurement for OAM modes. The single photons are then detected by detection means 3, preferably avalanche photon detectors and simultaneous two-photon events are identified by a coincidence logic 12. Finally, a complete quantum state tomography is performed.

We use a maximum-likelihood approach to estimate the physical density matrices of the detected photon pairs.

FIG. 2. Shows the setup. In the box 2 dim the generation of two-dimensionally entangled two-photon states is performed. Three-dimensional states are created together by elements in boxes 2 dim and +1 dim. Three non-linear crystals 1 are pumped with a continuous-wave laser beam 4 transmitted by a laser 10 at the central wavelength of 405 nm. Frequency-degenerate down -converted photons created by type II collinear SPDC propagate along identical paths 2 into the detection system with the polarizing beam-splitter 8 two spatial light modulators 9 and two detection means 3. Photons originating in second crystal 1 are created in I 2, 2 > OAM mode because of a spiral phase plate (SPP) 5 inserted after the first left polarizing beam splitter (PBS) 8 in the bottom of the left Mach-Zehnder interferometer. In addition, photons originating in the third crystal 1 are created in I - 2, -2 > mode due to the OAM sign flip element 5 that is implemented by an extra mirror not shown in Fig. 2. The pump beam 4 is filtered out of the output beam by wavelength dependence polarizing beam-splitter 8 or dichroic mirrors (DM) 16 and a band-pass filter 11.

Before detection, the two down -converted photons are separated on a polarizing beam-splitter 8 on the right in Fig.2. The state tomography of OAM degree of freedom is done by projective measurements where specific holograms are projected on two spatial light modulators (SLMs) 9 and reflected photons are coupled into single mode fibers and detected by detection means 3, preferably single photon counting modules. Resulting signals are post-processed by coincidence counting module 12. Relative phases fΐ and f2 can be adjusted by respective phase-shifters 6 implemented by a trombone system. Magnitudes of individual terms in the quantum state are controlled by setting the splitting ratio of the polarizing beam-splitters 8. The dichroic mirrors 16 on the top of the Mach-Zehnder interferometer can also be replaced by polarizing beam-splitters 8, reflecting the pump beam 4 and transmitting the down-converted photons. Lenses 7 are inserted in the pump beam 4 and down- conversion photon beam 2 to focus the beams in the crystals 1.

The main measurement results are listed in Tab. 1 below, shown as an example, where fidelities for different three-dimensionally (and also two-dimensionally) entangled states are presented. These example data demonstrate the full control over relative phases and magnitudes in the generated quantum states. The real and imaginary parts of density matrices for three of these states are also displayed in Fig. 3, where the theoretical expectations are represented by gray translucent bars. Most notably, we are able to create three orthogonal maximally entangled states I

I y₂ > and I y₃ > with average fidelity of 87,5 ± 0,6%. Orthogonality of these states does not follow directly from orthogonality of OAM modes, but indeed from different phase settings in individual states. State (see Tab. 1 and Fig. 3) demonstrates

the ability to adjust not only relative phases, but also relative magnitudes of terms in the quantum superposition. Average fidelity of three-dimensionally entangled states does not decrease significantly when compared to the average fidelity of 89,8 ± 0,5% for two-dimensional states. Coherence of entangled states thus does not suffer significantly when going from two to three dimensions and indicates the scalability of the approach for even higher dimensions. The coherence is limited by imperfect indistinguishability of the SPDC sources, slight misalignments, and imperfect transformations of OAM modes. Hlowever, none of these imperfections are of fundamental nature.

Table 1 shows the Fidelities between several chosen

two- and three-dimensionally entangled states and their realizations p. States

and form an orthonormal set of maximally entangled states in

three dimensions

State

is a manifestation of the ability to control not only relative phases in the quantum state, but also relative magnitudes.

Table 1 :

FIG. 3 shows three selected three-dimensionally entangled states. With the inventive method we can control the relative phases, as demonstrated in Fig. 3(a) and Fig. 3(b), as well as relative magnitudes, as can be seen in Fig. 3(c). Light gray and dark gray bars represent positive and negative values of reconstructed density matrices, respectively. Gray translucent bars represent the theoretical expectation. Fidelities of the measured states with their reference states are 87,0 ± 0,5%, 89,0 ± 0,4% , and 84,8 ± 0,8% respectively.

The state of Fig. 3(a) is

Scalability of the scheme is made possible by the modular structure of the setup, where adding a crystal 1 and a mode-shifter 5 results in an increase of the

entanglement dimension by one. In order to further improve the scalability, some modifications to the implementation can be made. We adopted the Mach-Zehnder interferometric configuration in the setup so that pump 4 and down-conversion beams 2 can be accessed separately. This leads to a number of interferometers scaling linearly with the required entanglement dimension. Furthermore, in the setup the mode-shifter 5 was inserted into the pump beam 4 of the second, and third crystals 2. The use of interferometers and higher-order-mode pumping can be avoided altogether by utilizing wavelength-dependent phase-shifters 6 and q-plates that leave the pump beam unaffected while manipulating only the down-conversion beam. The absence of interferometers leads to a simpler, more robust, and more compact design of the source. Such a scheme allows for fabrication of sources that display long-time stability, high brightness and very good quality of high-dimensionally entangled photon pairs.

The flexibility of the approach by producing several entangled quantum states in two and three dimensions could be demonstrated. The setup has a modular structure and in principle allows to generate entangled states in arbitrarily high dimension.

Several modifications of the setup are possible. Specifically designed optical elements can be used to construct truly scalable and simultaneously high-brightness quality two-photon sources. Such sources find a wide range of applications in fields like a future high-dimensionally quantum satellite-to-ground communication.

According to this preferred embodiment, the method uses OAM modes of light. Other specialized spatial mode families can be used as well. For example, guided modes can be utilized to optimize the entangled-state distribution over optical-fiber systems. Apart from phases and magnitudes, it is also possible with the setup to tune the coherence between the crystals arbitrarily, which enables one to generate custom- tailored high-dimensionally mixed states. This property allows for the investigation of, among others, bound-entangled states, such as those that were recently found to represent a counterexample to the longstanding Peres conjecture.

The method can be supplemented by techniques that use pump-beam shaping for high-dimensionally entanglement generation in order to create states entangled in significantly larger subspaces than is convenient with any of the two approaches individually. The very principle of coherent and indistinguishable SPDC processes presented here can be used in generation of multi-particle entangled states and could even lead to applications in special purpose quantum computation. In the following a more detailed and/or additional explanation and description of the scheme described above in Fig. 2 is given.

The simplified scheme of the setup shown in Fig. 2 described above does not show the implementation of the OAM sign flip element, variable splitting-ratio polarizing beam-splitters, phase shifters, and the interferometer stabilization system. In Fig. 5 the detailed scheme of the setup can be found. The OAM sign flip element is implemented by an extra mirror 17 inserted into the right interferometer in the +1 dim box. The variable splitting-ratio beam-splitter is built from the bottom polarizing beam splitters 8 and half-wave plates 13 in Fig. 5. After each polarizing beam-splitter 8 both beams 4 possess horizontal polarization.

Fig. 5 differs from Fig. 2 in the following manner. To phase-stabilize the

interferometer in the setup, an additional light beam emitted from an additional laser 15 at the central wavelength of 710 nm is injected into the unused input port of the polarizing beam-splitters 8. The two created spatial modes of additional light due to the Mach-Zehnder interferometer are recombined at the preferably dichroic mirror 16 and the resulting interfering beam is monitored by a detection means 3, preferably a fast photodiode. The detection signal is processed by a PID (proportional-integral- derivative) controller 20 and a feedback signal is fed to the piezoactuator-driven mirror 22 in order to compensate for phase fluctuations. For comparison, in Fig. 4 the time dependence of the coincidence count rate with and without stabilization is presented. This active feedback loop stabilization system also works as a fine phase shifter 6, for details see below. The coarse adjustment of the phase can be done by a trombone system 18 built in one arm of the interferometer. The trombone system 12 comprises four mirrors 16, two of them movable illustrated by the arrows in Fig. 5.

The OAM mode shifter 5 is inserted into the pump beam 4 instead of the down- converted beams, as suggested by the principle scheme in Fig. 1 , for the following reason. Requirements on the temperature of nonlinear crystals and on the

frequencies of down -converted photons did not allow for perfect collinearity of the generated pairs. In order to operate optimally the mode-shifter 5 has to be precisely centered with respect to the beam it acts upon. The failure to satisfy this condition for both photons of the pair leads to generation of undesirable higher-order OAM terms and a spread of the resulting OAM spiral spectrum.

FIG. 4. Shows the comparison of coincidence-count signal for the case when the interferometer in the setup is actively stabilized (dark solid line) and when it is not (dark dashed line). Photon pairs coming from the first and second crystals 1 , pumped with the beam 4 having zero quanta of OAM, were collected in time steps of one second. Gray shaded areas correspond to one standard deviation region of collected data when Poissonian counting statistics is assumed.

FIG. 5 shows the detailed setup. The two interferometers are phase-locked by active feedback systems. An additional laser diode 15 with central wavelength 710 nm is used to provide a locking-system beam that is injected into unused ports of bottom polarizing beam-splitters 8 and leaves the setup through the dichroic mirror 16. After filtering out the pump beam by an interference filter 19, the interference fluctuations of the additional laser diode 15 beam are detected by a fast photodiode detection means 3. The obtained signal is processed by a PID controller 20 and a feedback signal is sent to a piezo actuator 22 attached to one of the mirrors 18 in the interferometer. The relative phases of the down -converted beams (denoted by fΐ and cp2) can be adjusted by trombone systems 18 and by a proper setting of polarization of the corresponding additional beam. This is accomplished by a series of two quarter-wave plates 14 and one half-wave plate 13. Magnitudes of individual terms in the quantum state are controlled by setting the splitting ratio of the polarizing beam-splitters 8. A variable splitting-ratio beam-splitter is implemented by a polarizing beam-splitter 8 with two half-wave plates 13.

The generation of quantum states via the concept of entanglement by path identity requires coherent and indistinguishable photon-creation processes. To verify a sufficient level of coherence in the setup, the spiral phase plate was removed from the setup in Fig. 6 and the interference between different SPDC processes in the zero OAM mode was measured. The quality of the coherence is quantified by the interferometric visibility V = (Max (D) - Min (D)) / (Max (D) + Min (D)) where D is the coincidence count rate. Results for crystals A and B are shown in Fig. 2. The observed visibility exceeds 97% in this case and the two SPDC processes in crystals A and B thus exhibit a high degree of coherence. Analogous results were also obtained for crystals B and C.

In general, the following relation has to be satisfied in order to observe interference for collinear SPDC processes. Let L_¥h be the coherence length of the pump laser, which is in this case greater than 2 cm. Moreover, let

and L_P,B be the distances traveled by the pump beam from the beam splitter to crystals A and B, respectively. The physical conditions for coherence of corresponding SPDC processes are then given by:

where LSPDC is the propagation distance of down -converted photons from the first and second crystal 1. In other words, the optical path length difference between the two arms of the interferometer must be within the coherence length of the pump laser.

FIG. 7 shows two selected two-dimensionally entangled states as an example. Real and imaginary parts are shown. Dark gray and light gray bars represent positive and negative values of reconstructed density matrices, respectively. Transparent gray bars represent the theoretical expectation. Fig. 7(a) shows the State I

with fidelity 90,4 ± 0,5 %.

Fig. 7(b) shows the State with fidelity 89,1 ± 0,5 %.

Typically, the state of photon pairs

produced in an SPDC process contains a non-negligible admixture of higher-order OAM terms ··

Magnitudes of these contributions in general decrease for increasing OAM order. The precise relationship between the OAM order k and its complex amplitude ak is governed by several tunable parameters. In order for the scheme, to work properly, these parameters have to be chosen such that all higher-order OAM terms coming from the SPDC processes are significantly suppressed. As shown in Fig. 8 for the first crystal 1 , we were able to suppress the probability

of detecting the photons in the first OAM order below five percent of the probability of detecting them in the zero mode

Similar results were obtained for the second and third crystals 1. These example data justify the assumption that SPDC process produces photons only in their zero OAM mode.

FIG. 8 sows the normalized coincidences for different projective measurements of OAM in the computational basis. Photon pairs produced in the first crystal 1 , pumped with a beam 4 having zero quanta of OAM, were detected and coincidence counts collected for different choices of projections. On the two SLMs 9, see the detection system in Fig. 5, the wavefronts corresponding to OAM modes -2, . . ., 2 were projected. In the ideal case, only diagonal entries would be nonzero. The coincidence rate for 10, 0 > mode is more than twenty times higher than the next highest coincidence rate.

Relative phases in generated quantum states can be tuned precisely by a series of quarter- 14, half- 13, and quarter-wave plates14, henceforth referred to as the QHQ scheme, that are inserted into the additional laser beam as shown in Fig. 5. The QHQ scheme manipulates the local phase between the horizontal and vertical polarization components of the additional-laser beam. At the polarizing beamsplitter 8 the relative phase between polarizations translates into relative phase between the two modes of propagation of the additional-laser beam through the interferometer. After

recombination of the two paths at the dichroic mirror 16, the intensity of the interfering beam is measured by a photodiode 3, which feeds the measured signal to the PID controller 17. The controller interprets the intensity change as unwanted fluctuation and offsets the piezo actuator to compensate for it. This way the phase change is imprinted into the pump beam 4 and therefore into the down -converted photons as well.

When quarter-wave plates 14 in the QH scheme are rotated correctly, the middle half-wave plate 13 alone can be turned to adjust conveniently the phase in generated quantum states. In what follows, the working principle of QH scheme is explained. In Jones matrix formalism, a quarter-wave plate (Q) and a half-wave plate (H), rotated by angle a with respect to the vertical direction, are represented by

respectively, where R(a) is a rotation matrix and s_z is Pauli-Z matrix. Their forms read

First the working principle of the QHHQ scheme is explained, where two half-wave plates are used, and then shown that this scheme is equivalent to the QHQ scheme.

It can be shown that a single Q-wave plate and a single H-wave plate can be used to transform any elliptical polarization into a linear polarization. Such a linear

polarization can then be easily rotated by a half-wave plate independently of the input polarization. Finally, a quarter-wave plate rotated by

transforms a linearly polarized state with polarization angle f into an equally-weighted superposition of horizontal and vertical polarization components as

The polarization angle f is therefore transformed into a relative phase. In total,

scheme allows one to obtain a beam with polarization of the

form FI

where b and g depend on the input polarization as generated by the locking laser and relative phase

depends effectively only on the rotation angle a of the half-wave plate.

It is straightforward to prove two useful relations and

that

The extra s_z merely shifts the relative phase of the incoming beam by p, which is corrected for by the proper setting of b and g. We thus showed that

scheme can be used to adjust the relative phasein the state of the

additional-laser beam by turning the half- wave plate 13 appropriately.

Claims

Claims:

1. Apparatus for producing higher-dimensionally quantum-correlated and/or

entangled photon pairs, whereas the photon pairs are correlated and/or entangled in a spatial mode in dimension equal to or higher than three, whereas the apparatus comprises a pump laser (10) to pump a down- conversion crystal (1 ), and a two-dimension-module with at least one down- conversion crystal (1 ) pumped by the pump laser, and a mode-shifter (5) in order to produce two-dimensionally correlated and/or entangled photon pairs, whereas the apparatus further comprises one or more additional-dimension- module/s, whereas each additional-dimension-module in the apparatus adds one dimension to the produced two-dimensional correlated and/or entangled photon pairs,

whereas each additional-dimension-module comprises an additional down- conversion crystal (1 ) pumped by the pump laser (10) and by the before produced two-dimensional photon pairs, and an additional mode-shifter, whereas the two-dimensional correlated and/or entangled photon pairs and the pump laser are coherent in space and time in each additional down-conversion crystal (1 ),

whereas the mode-shifter (5) of the two-dimension-module and/or each additional-dimension-module

- is arranged in the pump beam (4) before the down-conversion crystal (1 ), and/or

- is arranged in the down-conversion photon pair path (2) after the down- conversion crystal (1 ).

2. An apparatus according to claim 1 ,

whereas the photon pairs are correlated and/or entangled in orbital angular momentum (OAM) or spin angular momentum (SAM).

3. An apparatus according to claim 2,

- is/are arranged in the pump beam (4) before the down-conversion crystal in order to add a quantum or quanta of OAM or SAM to the pump beam (4), and/or

- is/are arranged in the down-conversion photon pair path (2) after the down- conversion crystal (1 ) in order to add a quantum or quanta of OAM or SAM to the down-conversion photon pairs.

4. An apparatus according to one of the claims 1 to 3,

whereas one, or two, or three, or four, or five or more additional-dimension- modules are arranged in the apparatus, preferably are arranged in such a way, that the down-conversion photons of the two-dimension-module pass through the down-conversion crystals (1 ) of the one, or two, or three, or four, or five or more additional-dimension-module.

5. An apparatus according to one of the claims 1 to 4,

whereas the two-dimension module comprises a first and a second down- conversion crystal in order to produce coherent down-converted photon pairs.

6. An apparatus according to claim 5,

whereas the two-dimension module comprises a Mach-Zehnder interferometer in order to separate the pump beams of the first and second down-conversion crystals, and

whereas the photon pairs of the first down-conversion crystal and the pump beam are coherent in space and time in the second down -conversion crystal.

7. An apparatus according to one of the claims 1 to 6,

whereas the additional-dimension-module or each additional-dimension- module comprises at least one Mach-Zehnder interferometer in order to separate the pump beam of the additional down-conversion crystal from the pump beams of the before and/or behind arranged down-conversion crystals.

8. An apparatus according to claim 7,

whereas the additional down-conversion crystal is arranged in an output arm of the Mach-Zehnder interferometer, and/or within the Mach-Zehnder interferometer of the next additional-dimension-module.

9. An apparatus according to one of the claims 7 or 8,

whereas the additional down-conversion crystal is arranged within the Mach- Zehnder interferometer of the additional-dimension-module.

10. An apparatus according to one of the claims 7 to 9

whereas an additional laser beam is injected in the Mach-Zehnder

interferometer and the interfering beams of the additional laser are monitored behind the interferometer by a photodiode in order to stabilize the Mach- Zehnder interferometer by a piezo-actuator driven mirror or a phase-shift means.

11. An apparatus according to claim 5,

whereas the crystals in the two-dimension module and the mode-shifter are arranged so, that the pump beam and the down-conversion photon pair path overlap spatially in, and behind the crystal.

12. An apparatus according to claim 11 ,

whereas the additional-down-conversion crystal and the additional-mode- shifter are arranged so, that the pump beam and the down-conversion photon pair path overlap spatially before, in, and behind the additional-down- conversion crystal.

13. An apparatus according to one of the claims 1 to 12,

whereas the apparatus comprises at least one phase shifter arranged in the pump beam before the down-conversion crystal in order to change the phase in the pump beam, or in the down-conversion photon pair path behind the down-conversion crystal in order to change the phase of the photon pair.

14. An apparatus according to one of the claims 1 to 13,

whereas the mode shifter of the two-dimension-module and/or each additional- dimension-module is a spiral phase plate, or a liquid crystal, or a sign switch comprising a mirror, or a vortex phase plate, or a q-plate, or a spatial light modulator (SLM) in order to add a quantum or quanta of OAM or SAM to the pump beam photons or the down-conversion photon pairs.

15. Method to provide higher-dimensionally quantum correlated and/or entangled photon pairs, whereas the photon pairs are correlated and/or entangled in a spatial mode in dimension equal or higher than three,

whereas the method comprises the steps of

I) providing two-dimensionally correlated and/or entangled photon pairs by a two-dimension-module comprising at least one down-conversion crystal pumped by a pump beam of a pump laser and a mode-shifter,

II) adding one or more dimension to the two-dimensionally quantum correlated and/or entangled photon pairs by passing the pump beam and the two- dimensionally correlated and/or entangled photon pairs through one or more additional-dimension-module/s in order to add one additional dimension to the two-dimensionally correlated and/or entangled photon pairs by each

additional-dimension-module,

whereas the two-dimensionally correlated and/or entangled photon pairs and the pump beam are coherent in space and time in each additional down- conversion crystal,

whereas each additional-dimension-module comprises an additional down- conversion crystal pumped by the pump beam and an additional mode-shifter.

16. Method according to claim 15,

whereas the mode-shifter of the two-dimension-module and/or each additional- dimension-module

- is arranged in the pump beam before the down-conversion crystal in order to add a quantum or quanta of OAM or SAM to the pump beam, and/or

- is arranged in the down-conversion photon pair path after the down- conversion crystal in order to add a quantum or quanta of OAM or SAM to the down-conversion photons.

17. Method according to one of the claims 15 or 16,

whereas in step II) one, two, three, four, five or more dimensions are added by one, two, three, four, five or more additional-dimension-modules, preferably are arranged in such a way, that the down-conversion photon pairs of the two- dimension-module passes through the down-conversion crystals of each additional-dimension-module.

18. Method according to one of the claims 15 to 17,

whereas in step I) a first and a second down-conversion crystal are provided in order to generate the two-dimensionally down-converted photon pairs.

19. Method according to claim 18,

whereas in step I) the two-dimension-module comprises a Mach-Zehnder interferometer in order to separate the pump beams of the first and second crystals, and

20. Method according to one of the claims 15 to 19,

whereas in step II) the additional-dimension-module comprises a Mach- Zehnder interferometer separating the pump beam of the additional down- conversion crystal from the pump beams of the before and/or behind arranged down-conversion crystals.

21. Method according to claim 20,

whereas the additional down-conversion crystal is arranged and pumped in an output arm of the Mach-Zehnder interferometer, and/or in the Mach-Zehnder interferometer of the next additional-dimension-module.

22. Method according to claim 20,

whereas the additional down-conversion crystal is arranged in the Mach- Zehnder interferometer of the additional-dimension-module.

23. Method according to one of the claims 18 to 22,

whereas an additional laser beam is injected in the Mach-Zehnder

interferometer and the interfering beams of the additional laser are monitored behind the interferometer by a photodiode in order to stabilize the Mach- Zehnder interferometer by a piezo-actuator driven mirror.

24. Method according to one of the claims 15 or 18,

whereas in step I) the two-dimension module comprises a first and a second down-conversion crystal in order to produce coherent down -converted photon pairs.

25. Method according to claim 24,

whereas in step II) the additional-down-conversion crystal and the additional- mode-shifter are arranged so, that the pump beam and the down-conversion photon pair path overlap spatially before, in, and behind the additional-down- conversion crystal.

26. Method according to one of the claims 15 to 25,

whereas the apparatus comprises at least one phase shifter arranged in the pump beam before the down-conversion crystal, or in the down-conversion photon pair path behind the down-conversion crystal in order to change the phase.

27. Method according to one of the claims 15 to 26,

28. Method according to one of the claims 15 to 28,

whereas the method provides higher-dimensionally quantum correlated and/or entangled photon pairs for a communication channel between two parties.

29. Method according to claim 28,

whereas the two photons of each photon pair are

- collinear and separated by a polarizing beam splitter, or by a wavelength dependent means, preferably a wavelength dependent mirror or

- non-collinear,

30. Method according to one of the claims 28 or 29,

whereas each party detects the higher-dimensionally quantum correlated and/or entangled photons in a detection module, comprising an optical measurement means to measure the OAM or SAM or another spatial mode, preferably at least a spatial light modulator (SLM) or an interferometer, or a mach-zehnder interferometer with Dove-prism or a diffractive optics element such as multi-plane-light-conversion as optical measurement means and a single photon detector.

31. A communication apparatus, whereas the communication apparatus

comprises a communication channel between two parties,

whereas the communication apparatus comprises further an apparatus according to one of the claims 1 to 14 providing higher-dimensionally quantum correlated and/or entangled photon pairs for the communication between the parties.

32. A communication apparatus according to claim 31 ,

comprising a polarizing beam splitter or a wavelength dependent means, preferably a wavelength dependent mirror for the separation of the two photons of each photon pair.

33. A communication apparatus according to one of the claims 31 or 32,

with two parties each comprising a detection module with at least a spatial light modulator (SLM) and a single photon detector for the detection of the higher-dimensionally quantum correlated and/or entangled photons.