DE102010020817A1 - Method for transmission of information about polarization state of photons to stationary system used in e.g. quantum cryptography field, involves assigning states based on polarizations, and arranging quantum system in superposition state - Google Patents

Method for transmission of information about polarization state of photons to stationary system used in e.g. quantum cryptography field, involves assigning states based on polarizations, and arranging quantum system in superposition state

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Publication number
DE102010020817A1
DE102010020817A1 DE201010020817 DE102010020817A DE102010020817A1 DE 102010020817 A1 DE102010020817 A1 DE 102010020817A1 DE 201010020817 DE201010020817 DE 201010020817 DE 102010020817 A DE102010020817 A DE 102010020817A DE 102010020817 A1 DE102010020817 A1 DE 102010020817A1
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state
states
quantum
superposition
photons
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DE201010020817
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German (de)
Inventor
Jens Förstner
Dirk Mantei
Steffen Michaelis de Vasconcellos
Prof. Dr. Zrenner Artur
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Universitaet Paderborn
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Universitaet Paderborn
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Priority to DE201010020817 priority Critical patent/DE102010020817A1/en
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    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04LTRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00Cryptographic mechanisms or cryptographic arrangements for secret or secure communication
    • H04L9/08Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
    • H04L9/0816Key establishment, i.e. cryptographic processes or cryptographic protocols whereby a shared secret becomes available to two or more parties, for subsequent use
    • H04L9/0852Quantum cryptography
    • HELECTRICITY
    • H04ELECTRIC COMMUNICATION TECHNIQUE
    • H04BTRANSMISSION
    • H04B10/00Transmission systems employing electromagnetic waves other than radio-waves, e.g. infrared, visible or ultraviolet light, or employing corpuscular radiation, e.g. quantum communication
    • H04B10/70Photonic quantum communication

Abstract

The invention relates to a method for transmitting the state of polarization of photons in a stationary system in which a quantum system is excited with photons of a polarization state, which has two states that are excitable with mutually orthogonal polarizations and whose energetic distance is smaller than the energetic Range of photons, both states are occupied in dependence on the polarization and the quantum system assumes a superposition state of both states.

Description

  • The invention relates to a method for transmitting the polarization state of photons in a stationary system.
  • The field of application of the invention is, for example, in the field of quantum information processing or quantum information processing, here z. As the quantum cryptography, quantum communication and quantum computer.
  • In these technical application areas, information that is carried by photons should be stored and possibly manipulated or retrieved. The information that can be transmitted by photons is essentially given by their polarization state, which can be represented mathematically by a vector of the Poincaré sphere. This type of representation is common in the art and known.
  • Although it is known that atoms and molecules can be excited by photons in an energetically higher state and that such excitation is also polarization-dependent, nevertheless, the excited state does not exactly represent the polarization of the exciting photon and thus the information carried. Thus, namely, an electronic state, the z. B. linear horizontal polarization can be excited not only be occupied when the excitation is done by a photon with exactly linear horizontal polarization, but with a probability even if the photon has at least a linear horizontal polarization component. Thus, it becomes clear that the information about the polarization state of a photon can not readily be taken from the generated excited state. In the case described, it can only be deduced from the excited state that the exciting photon had a certain horizontal polarization component, but not how large it was and how exactly the vector of the associated Poincaré sphere was aligned.
  • It is therefore the object of the invention to provide a method with which exact information about the polarization state of a photon can be imaged in a stationary system. In this case, the polarization state of the photon, which is described by the Poincaré sphere, is preferably to be mapped into the system, that is, by a description of the state of the system, as it were, the Poincaré sphere of the exciting photon is also represented.
  • This object is achieved in that a quantum system is excited with a photon of a polarization state, which has two states that can be excited with mutually orthogonal polarizations and whose energetic distance is smaller than the energetic bandwidth of the photons, both states depending are occupied by the polarization and the quantum system assumes a superposition state of both states.
  • The main idea is to excite with a photon two so-called orthogonal states, which are coupled to each other via the quantum mechanical system, in particular via the occupation. Since each polarization of a photon can be described by the superimposition of two orthogonal polarization states, one possibility thus results by exciting two electronic states, which can be excited by mutually orthogonal polarizations, to represent the polarization state of the original exciting photon. Vertical polarizations are z. B. linear horizontal and vertical polarizations as well as circular right and left rotating polarizations.
  • Classically, such a system results in an arrangement of two orthogonal polarization-sensitive oscillators, which are triggered by the photon and whose initial phase difference in the light-matter interaction is determined by the polarization state.
  • Due to the energetic difference between the two coupled oscillators results in a beat frequency, in which the original state is reproduced after each beat period, but is determined deterministically at all other times. Thus, such an excited quantum mechanical system completely represents the original polarization state of the exciting photon. Ie. Figuratively speaking, the Poincaré sphere has been imaged in this system.
  • In a preferred embodiment, it may be provided that the quantum system is formed by a quantum bit whose fine-structure-split ground state forms two orthogonal states which can be excited with mutually orthogonal polarizations.
  • Under a quantum bit or short qubit is understood in the art, any manipulatable 2-level quantum system, z. B. an exciton in the semiconductor quantum dot. However, this term does not specifically indicate the number of possible states that this system can assume. Every quantum mechanical system of this kind can in principle assume an infinite number of superposition states, but in general the state of a Such a quantum system can not be reliably determined by a measurement; rather, the probability of a measured value is determined by the state of the quantum bit present before the measurement.
  • The designation as a 2-level quantum bit results essentially from the fact that such a quantum bit has only two so-called eigenstates, which can be reliably distinguished by measurement.
  • Considering therefore a quantum bit in comparison to a classical memory bit, so in a quantum bit exactly one classic bit can be stored, since only two states, previously referred to as eigenstates, are safely distinguishable from each other.
  • However, the advantage of the quantum bits lies precisely in the existence of the further states, even if they can not be distinguished by a measurement, since these existing states can be used at least for times before a measurement, for example for calculations. For example, quantum bits in quantum computer science form the basis for quantum computers as well as for quantum cryptography. A quantum bit, which is designed as a 2-level system, thus forms the smallest possible storage unit for a quantum state and at the same time defines a measure of the quantum information.
  • The states of a quantum bit can be represented as the points on the surface of a sphere in three-dimensional space, called the Bloch sphere. These states on the surface of the sphere form the so-called pure states, whereby through interactions fundamentally also mixed states are possible, which are represented by points inside the sphere.
  • The measurement of the state of a quantum bit can be understood in this representation image as the projection of the point on the surface or in the interior of the sphere on the center straight line of the Bloch sphere, which connects the two orthogonal eigenstates, which are thus opposite to each other on the spherical surface , The result of the projection therefore represents the probability of the condition and thus the result of the condition measurement.
  • According to the invention, it is provided to use a quantum bit whose total potential is asymmetrically z. B. is elliptical so as to form the orthogonal states. Thus, such an asymmetrical quantum bit does not represent a 2-level system, but a 3-level system, of which 2 states are coupled to each other via the third state. Such a fine structure splitting can, for. B. result from an unbalanced total potential. For example, the unbalanced total potential can also be generated by applying an electric and / or magnetic field around the quantum bit so as to effect a Zeeman or Stark effect.
  • The splitting of at least one level involved in each case leads to two orthogonal, d. H. states excitable by two orthogonal polarizations. Such a quantum bit with a split state can be represented by two Blochkugeln, wherein each Blochkugel is assigned to one of the two orthogonal states. Thus, according to the invention, a Poincaré sphere representing the photon is mapped into the two orthogonal states of the qubit, respectively its superposition state, represented by two Bloch spheres.
  • According to the invention, furthermore, the qubit can be selected such that a coherent electron-hole pair is formed by excitation with a photon, which assumes a superposition state of both orthogonal states that depends on the polarization state of the photon. The lifetime of such an electron-hole pair can be increased by applying an external electric field by electron and hole are separated in the space of the qubit.
  • In an advantageous development of the method, it can be provided that the superposition state is changed by at least one gate manipulation, in particular by laser pulses.
  • The gate manipulation of a Bloch sphere is understood here to mean that the Bloch vector, which describes the state of the quantum bit in this Bloch sphere and thus originates from the center of the Bloch sphere and ends in the surface of the sphere, changes in its end point becomes. The axis of rotation and the rotational distance are predetermined among others by the phase and amplitude of the laser pulses. The selection of Blochkugel to be manipulated takes place via the polarization of the laser pulse.
  • The gate manipulation is performed, for example, so that it acts on the superposition state of both orthogonal states of the quantum bit. In particular, the gate manipulation can also be selected such that only one of the two Bloch spheres is changed or both simultaneously.
  • A special form of such a gate manipulation z. B. the so-called Hadamard gate which changes a Bloch vector by Pl / 2, or 90 degrees within the Blochkugel.
  • It proves to be advantageous here that, starting from the "stored" photon state in the stationary system of the quantum bit, changes can now be made by gate manipulation in the following. Therefore, z. B. in use as quantum register operations are represented by the Gatemanipulationen.
  • An initially stored superposition state, as well as a superposition state changed by at least one gate manipulation, can be rehearsed by a measurement according to the invention.
  • For performing the measurement, for example, an electric field may be applied around the quantum system, or an applied electric field may be changed, and the current generated thereby detected, in particular, the electron-hole pair being separated by the field.
  • In another embodiment, provision may also be made for the emission of photons to be stimulated by irradiation of photons into the quantum system, in particular the polarization of incident photons being selected as one of the two polarizations, with which one of the two states is selective is excitable.
  • In a particularly preferred embodiment of the invention, at least one gate manipulation can be carried out prior to the measurement and selected with respect to a presumed superposition state such that the measurement of the manipulated superposition state provides an expected measurement result only when the presumed previous superposition state is actually present.
  • This method variant is based on the fact that a measurement result with quantum bits is only reliable if an eigenstate of the quantum bit or here both Blochkugeln has been present before the measurement. It is therefore advantageous for checking which superposition state is present before the measurement to perform such gate manipulations, which, starting from a presumed superposition state, convert this state and thus both Bloch spheres into an eigenstate. If the measurement result corresponds to this eigenstate, then it can be reliably concluded that the assumed superposition state actually existed.
  • If, on the other hand, the measurement result does not correspond to the eigenstate, then it can be concluded from this that the assumed superposition state was not present.
  • This method variant makes it possible to obtain a best possible statistical relevance of the measurement result with a minimum number of individual measurements from a sequence of temporally separated, similar individual measurements.
  • Preferably, the transmission of a polarization state and / or the gate manipulation of a generated superposition state can be effected by illumination of a quantum bit with laser pulses. In such an application, a development opens in which the two orthogonal states of a multiplicity of identical quantum bits are excited by means of a laser pulse and the superposition states of at least some, in particular all quantum bits are manipulated in a different manner and the manipulated superposition states are measured by gate manipulations. Thus, the same information is initially stored simultaneously in all quantum bits, but after the manipulations each quantum bit has a different superposition state.
  • If, during the measurement of one of the quantum bits, a result that corresponds to an eigenstate can be deduced from this measurement result, which superposition state the quantum bit had before the manipulation of the gate, since it is known which gate manipulation was applied to this quantum bit. Thus, the superposition state before the gate manipulation corresponds to that which is obtained if the eigen state is applied to the inverse gate manipulation which led to the above-mentioned result in the case of this quantum bit in the measurement.
  • Thus, the performance of the gate manipulations may be performed such that the various gate manipulations are selected according to different presumed superposition states such that out of the plurality of measured changed superposition states of the quantum bits only the measurements of those quantum bits of the plurality of expected measurement results provide their superposition states prior to the change the suspected corresponded.
  • From such a measurement of several quantum bits, which are in the same state, a statistically significant statement about their condition can already be obtained by a single measuring operation on these quantum bits. A time repetition of identical individual measurements to obtain statistical significance, as described using the example of the measurement on a single quantum bit, can thus advantageously be avoided.
  • The invention will be described by way of example with reference to the following figures. Show it:
  • 1 : a quantum system with two orthogonal states
  • 2 : the implementation of the procedure
  • 1 shows in a symbolized representation of a quantum system that is suitable for carrying out the method. Visible is a 3-level system achieved by a fine structure splitting whose two states X> and Y> have an energetic distance E FSS due to the fine structure splitting.
  • Each of the two levels X> or Y> can be excited by a linear polarization. The polarization direction that excites the X> level is perpendicular to the direction of polarization, which excites the Y> level. Therefore, the two levels are also called orthogonal states. The occupation of each of the two states can be represented by an associated Bloch sphere, each above the two states in the 1 is shown.
  • The 2 shows the application of a first laser pulse for storing information about the polarization and a second for performing a gate manipulation in the effect on such a quantum system of 1 , In the example, both laser pulses are designed as Hadamard pulses to simplify the illustration, ie they rotate the Bloch vector by 90 degrees each time from its previous position. The embodiment of the invention is not limited to these types of pulses.
  • The 2 shows that with a linear horizontal polarization a quantum bit is excited with a fine structure splitting. Because of this fine structure splitting, there are two levels X> and Y> that can be excited polarization-selectively.
  • With the linear horizontal polarization, which is represented in the Poincaré sphere with a vector under alpha = 0, only one of the two levels, namely here the level X> is excited. On the other hand, a linear vertical polarization with alpha = 90 degrees would exactly excite only the other level Y>.
  • Thus, with the first laser pulse of polarization alpha = 0, due to the fact that it is a Hadamard pulse, the Bloch vector of the Bloch sphere is rotated to the X> state from the w axis to the v axis. Thus, there is an occupation N = 1/2 for the X> state. The Y> state remains unchanged since the wrong direction of polarization was present at the stimulating pulse.
  • As a result, it can be seen that the entire information content of the Poincaré sphere is clearly converted into the superposition state of the two individual states X> and Y>. Only exactly the aforementioned polarization leads to this occupation of both states.
  • The gate manipulation with the second pulse and the linear polarization beta = 0 leads in the figure to a further rotation of the Bloch vector for occupation N = 1 of the X> state. The Y> state remains unchanged because of the non-matching polarization with the occupation N = 0. This results in an eigenstate of the quantum bit.
  • Would now this quantum system thus produced rehearsed, z. B. by applying a voltage around the system, so would result in a maximum current indicating a maximum occupation of N = 1. Due to the fact that we know the probing laser pulse and we know that it rotates only the Bloch vector of the X> state by 90 degrees, we can conclude that the X> state was previously N = 1/2 and the Y> State was occupied with N = 0.
  • This results in the possibility to deliberately rehearse a suspected state of the Blochkugeln and thus a suspected state of the Poincaré sphere by a Gatemanipulation which shows an expected result only if the suspected state before the Gatemanipulation existed.

Claims (11)

  1. A method for transmitting the polarization state of photons in a stationary system, characterized in that photons of one polarization state, a quantum system is excited, which has two states which are excitable with mutually orthogonal polarizations and whose energetic distance is smaller than the energy bandwidth of Photons, where both states are occupied as a function of the polarization and the quantum system assumes a superposition state of both states.
  2. A method according to claim 1, characterized in that the quantum system is formed by a quantum bit, the fine structure split ground state forms two orthogonal states that can be excited with mutually orthogonal polarizations, in particular wherein the orthogonal states are generated by forming a single-ended, in particular elliptical total potential of the quantum bit ,
  3. Method according to one of the preceding claims, characterized in that the unbalanced total potential by applying a electric and / or magnetic field around the quantum bit is generated.
  4. Method according to one of the preceding claims, characterized in that by excitation with a photon, a coherent electron-hole pair is formed, which assumes a dependent of the polarization state of the photon superposition state of both orthogonal states.
  5. Method according to one of the preceding claims, characterized in that the superposition state is changed by at least one gate manipulation, in particular by laser pulses.
  6. Method according to one of the preceding claims, characterized in that the superposition state is rehearsed by a measurement.
  7. A method according to claim 6, characterized in that for performing the measurement, an electric field is applied to the quantum system or an applied electric field is changed, wherein the electron-hole pair is separated and the current thereby generated is detected.
  8. A method according to claim 6, characterized in that for carrying out the measurement, the emission of photons is stimulated by irradiation of photons in the quantum system, in particular wherein the polarization of incident photons is selected as one of the two polarizations with which one of the two states is selectively excitable ,
  9. Method according to one of the preceding claims, characterized in that at least one gate manipulation is performed prior to the measurement and is selected with respect to a suspected superposition state that the measurement of the manipulated superposition state provides an expected measurement result only in the actual presence of the presumed previous superposition state.
  10. Method according to one of the preceding claims, characterized in that the transmission of a polarization state and / or the manipulation of a generated superposition state by illumination with laser pulses.
  11. Method according to one of the preceding claims, characterized in that by means of a laser pulse, the two states of a plurality of identical quantum bits are excited and manipulated gate manipulations the superposition states of at least some, in particular all quantum bits differently and the manipulated superposition states are measured, in particular such that the various gate manipulations are selected according to different presumed superposition states, and from the plurality of measured changed superposition states of the quantum bits, only the measurement of that quantum bit of the plurality gives an expected measurement result whose superposition state before the change was the presumed one.
DE201010020817 2010-05-18 2010-05-18 Method for transmission of information about polarization state of photons to stationary system used in e.g. quantum cryptography field, involves assigning states based on polarizations, and arranging quantum system in superposition state Withdrawn DE102010020817A1 (en)

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Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
DE10013184A1 (en) * 2000-03-17 2001-09-20 Deutsche Telekom Ag Selective photon polarization method for quantum processor involves activating electrooptical modulator in specific time, during which probability of presence of photon is maximum
DE10037652A1 (en) * 2000-07-31 2002-02-14 Deutsche Telekom Ag Process for transferring moment of momentum to double refracting object made of mercury halide and/or Kevlar comprises changing polarizing state of light as polarized light passes through object
US6678379B1 (en) * 1999-06-18 2004-01-13 Nec Corporation Quantum key distribution method and apparatus

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6678379B1 (en) * 1999-06-18 2004-01-13 Nec Corporation Quantum key distribution method and apparatus
DE10013184A1 (en) * 2000-03-17 2001-09-20 Deutsche Telekom Ag Selective photon polarization method for quantum processor involves activating electrooptical modulator in specific time, during which probability of presence of photon is maximum
DE10037652A1 (en) * 2000-07-31 2002-02-14 Deutsche Telekom Ag Process for transferring moment of momentum to double refracting object made of mercury halide and/or Kevlar comprises changing polarizing state of light as polarized light passes through object

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
KOSAKA,H.,et.al.:Coherent transfer of light polarization to electron spins in a semiconductor-toward quantum media conversion-.In:IEEE Lasers and Electro-Optics,CLEO 2008,Conference on,Piscataway,NJ,USA ganze Schrift *

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