JP6483643B2 - Quantum state measurement device - Google Patents

Description

  The present invention relates to a quantum state measurement device that measures time position quantum states.

  Quantum mechanical binary states in which 0 and 1 correspond to polarization states and time position states of photons, which are conventionally called qubits, are studied in quantum information processing technology such as quantum cryptography, quantum teleportation, and quantum computing. It has On the other hand, high-dimensional quantum states in which single photons exist in a Hilbert space of more than two dimensions, which is called qudit in recent years, are drawing attention. This is a mapping of information using d types (d> 2) of mutually orthogonal states with respect to the time position of photons, orbital angular momentum, frequency and the like. It is known in Non-Patent Document 1 that using a large dimension of qudits for quantum information processing improves the resistance to noise, for example, in the case of quantum cryptography.

  In performing quantum information processing, it is necessary to prepare high quality and appropriate quantum states according to the information processing used. The technique of quantum state measurement used to evaluate this prepared state is quantum state tomography. More specifically, quantum state tomography is a technique for measuring the quantum state density function ρ of the object to be measured.

Quantum state tomography can be roughly divided into a method of reconstructing a quantum state density function by linear transformation of measured data, and one of the physically acceptable parameters of the quantum state density function that has the smallest error from the measured data There is a method of obtaining by optimization by numerical calculation. Here, the latter case will be described. For simplicity, we will describe here the quantum state tomography in the case of two-dimensional time position quantum states. Assuming that a state vector representing a state in which a single photon exists at time position t ₀ is | 0> and a state vector representing a state existing at time position t ₁ is | 1>, the quantum state of a two-dimensional time position quantum state The density function can be expressed as the following equation.

However, since c _{i, j} is a parameter for determining the quantum state density function and ρ is a Hermitian operator, c _0,0 and c _1,1 are real numbers and c _0,1 and c _1,0 are , C _0,1 = c _1,0 ^* ( ^* is a complex conjugate). In addition, c _0,0 + c _1,1 = 1 because the sum of probabilities is 1.

Since c _{i, j} can be regarded as an element of a matrix, the above equation can be expressed as follows.

What we do in quantum state tomography is to estimate all c _{i, j} from experimental results. Here, the real parameters that must be obtained from the above-described conditions that c _{i, j} should satisfy are c _0,0 , c _R = Re (c _0,1 ), c _I = Im (c _{0 , 1} ) (where Re and Im are functions for extracting the real and imaginary parts, respectively). Therefore, if the results for at least three different measurements are obtained, the value of the quantum state density function can be estimated. In actual experiments, since the obtained data is not probability but frequency data, four different measurements are performed to obtain the sum of frequencies corresponding to the sum of probabilities 1. As four types of measurements, projective measurements to the state | 0>, | 1> and the two states | L> and | D ⁺ > defined below are often used.

Here, the projective measurement operator P ₀ = | 0 〈0 、, P ₁ = | 1 〈1 P, P _L = L L 〈L 、, P _{D +} = D D ⁺ 〈 ⁺ D ⁺ | Do. The expected values n ₀ ^p , n ₁ ^p , n _L ^p , n _{D +} ^p of the measurement frequency obtained when these measurements are performed for N photons having a state density function は, “n ₀ ^p = NTr (P ₀ )) (5), “n ₁ ^p = NTr (P ₁ )) (6)”, “n _L ^p = NTr (P _L )) (7) “N _{D +} ^p = NTr (P _{D +} ))” (8) ”. Tr (x) is a trace of x.

If the errors between these theoretically expected expectations and the experimental results are evaluated, and N, c ₀ , ₀ , c _R , c _I such that the error is minimized can be obtained by numerical optimization, The density of states function can be determined by equation (2).

As the evaluation of the error, the theoretically predicted frequency vector n ^p = (n ₀ ^p , n ₁ ^p , n _L ^p , n _{D +} ^p ) and the corresponding frequency vector of the experimental result n ^e = (n ₀ ^e , N ₁ ^e , n _L ^e , n _{D +} ^e ), and there is a method of minimizing the Euclidean distance.

Moreover, as an evaluation of the error, a method of minimizing the likelihood function χ (n ^p ) determined by the following equation is generally used.

  In addition, in the expression of に よ る by the equation (2), since it often becomes a non-physical state density function depending on the setting of parameters, the following expression is also used as ρ.

  In fact, Patent Document 1 and the like are known as a method of performing this quantum state tomography on a two-dimensional time position quantum state.

The above is the basic contents of quantum state tomography. If we want to extend the above contents to other states, for example, quantum state tomography of d-dimensional n photons, we use d ⁿ × d ⁿ Hermitian matrix as state density function 、, d ²ⁿ different simultaneous measurement operators as measurement operators, By replacing the above discussion with a frequency vector of length d ^{2 n} corresponding to the simultaneous measurement, quantum state tomography of d-dimensional n photons becomes possible.

  Quantum state tomography in the case of qubits is widespread, but quantum state tomography in the case of qubits is still unreported. Specifically, quantum state tomography in the case of qudits has been reported in which the state is encoded in the orbital angular momentum of a photon and the state is encoded in the frequency of the photon.

JP 2008-225341 A

N. J. Cerf et al., "Security of Quantum Key Distribution Using d-Level Systems", Physical Review Letters, vol. 88, no. 12, 127902, 2002. T. Ikuta and H. Takesue, "Enhanced violation of the Collins-Gisin-Linden-Massar-Popescu inequity with optimized time-bin-entangled ququarts", Physical Review A, vol. 93, no. 2, no. 2, 022307, 2016.

As described above, in order to perform quantum state tomography, measurement corresponding to the superposition of time positions corresponding to | L> and | D ⁺ > in the case of qubits, and time position state | 0> , | 1> needs to be measured. Non-Patent Document 2 is known as an implementation method of measurement corresponding to the superposition state in the case of a high dimensional time position quantum state. However, as described later, in the prior art, it is difficult to perform measurement corresponding to the time position state using a Mach-Zehnder interferometer or the like.

  In addition, as a common drawback to the methods presented so far, there is the disadvantage that the setup for actually performing the measurement must be changed by the same number as the types of measurements required to perform quantum state tomography. Exists.

In the conventional measurement, when a filter is provided in front of the photon detector and the photon is detected by the photon detector after passing through the filter, it is determined that the photon is in the quantum state defined by the filter. . For example, in the two-dimensional case, if a filter that transmits only photons of state | 0> is used, this filter is used in Equation (5), Equation (6), Equation (7), and Equation (8). Among the projection measurement operators, there is defined a measurement by P ₀ .

Thus, in a measurement using a filter that transmits only a specific state, only one specific state is covered in one measurement. In the above example, in order to perform measurements on other three states other than P ₀ will be measured by changing the filter corresponding to each state.

Since the type of measurement required for quantum state tomography is d ² for dimension d, the larger the dimension, the greater the number of measurements required, and the more likely it is the effect of measurement setup errors to accumulate. It will lead to errors and deterioration to the measured condition.

  The present invention has been made to solve the problems as described above, and it is an object of the present invention to reduce the error and deterioration of measurement results and to enable the measurement of the quantum state more easily.

  The quantum state measuring device according to the present invention is a quantum state measuring device for measuring the time position quantum state of a four-dimensional time position single photon having four time positions where photons can exist and a predetermined time position interval T. , The delay time difference between the two paths is 2T, the phase difference between the two paths can be set to 0 or π / 2, and a Mach-Zehnder type 1st one receives a four-dimensional time position single photon The delay interferometer and the input end are connected to the output end of one of the first delay interferometers to be cascaded, and the delay time difference between the two paths is T, and the phase difference between the two paths is Mach-Zehnder type second delay interferometer which can be set to 0 or π / 2, photon detector for detecting arrival time of photon output from one output end of second delay interferometer, and first delay interference The phase difference in the measurement is 0, and the second delay interferometer Let the phase difference in the first delay interferometer be π / 2, the phase difference in the second delay interferometer be 0, and the phase difference in the first delay interferometer be π / 2. Under the third measurement condition, the arrival time of the photon detected by the photon detector under the second measurement condition and the phase difference in the first delay interferometer are 0, and the phase difference in the second delay interferometer is π / 2 The photon detector under the fourth measurement condition where the arrival time of the photon detected by the photon detector and the phase difference in the first delay interferometer are π / 2 and the phase difference in the second delay interferometer is π / 2 And a processing unit which records the arrival time of the detected photon for each measurement condition, and obtains the time position quantum state of the four-dimensional time position single photon from the information about the frequency of the arrival time for each measurement condition recorded.

Further, another quantum state measuring apparatus according to the present invention measures the time position quantum states of d-dimensional time position n photons having d time positions at which n photons can be present and a predetermined time position interval T. State-of-the-art measuring device, which is connected in cascade to each output port of the optical demultiplexer, and an optical demultiplexer that inputs d photons at n-dimensional time position n and outputs n photons to different output ports One of the multistage interferometers is connected to n multistage interferometers consisting of K type (K is the smallest integer greater than log ₂ d) Mach-Zehnder type delay interferometers and n multistage interferometers. K comprising n photon detectors for detecting arrival times of photons output from the output end and a processing unit for recording arrival times of photons detected by the photon detectors, and configuring each multistage interferometer Delay interferometers of different types have different delay time differences between the two paths. is a ^{k T (0 ≦ k ≦ K} -1), K species of the delay interferometer constituting each of the multi-stage interferometer, the phase difference between the two paths is settable to zero or [pi / 2, the processing The unit has a maximum of K2 ^K + (K + 1) d kinds of temporally different detection signals for each photon detected by each photon detector and a phase difference of 0 or π / 2 set in each delay interferometer. The arrival time of 2 ^Kn {K2 ^K + (K + 1) d} ⁿ kinds of signals is recorded for each measurement condition from the measurement of a plurality of measurement conditions by combination of 2 ^K kinds of phases by. From the information on the frequency of time, the time position quantum state of the d-dimensional time position n photon is determined.

  In the above-described quantum state measurement apparatus, in addition to the photon detector connected to one of the last stage delay interferometers connected in cascade, an output to which the delay interferometers of the subsequent stages of delay interferometers other than the last stage are not connected A photon detector connected to the end may be provided.

  In the above-described quantum state measuring apparatus, the processing unit corrects the frequency of arrival time based on the waveguide loss and deviation of the branching ratio depending on the path in the delay interferometer, which has been measured in advance, to obtain the time position quantum state. It is good to ask for

  As described above, according to the present invention, an excellent effect can be obtained that the error and deterioration of the measurement result can be reduced and the quantum state can be measured more easily.

FIG. 1 is a configuration diagram showing a configuration of a quantum state measurement device according to Embodiment 1 of the present invention. FIG. 2 is a block diagram showing the configuration of the quantum state measuring apparatus according to the second embodiment of the present invention. FIG. 3 is a block diagram showing the configuration of the quantum state measuring apparatus according to the third embodiment of the present invention.

  Hereinafter, embodiments of the present invention will be described with reference to the drawings.

First Embodiment
First, the first embodiment of the present invention will be described with reference to FIG. FIG. 1 is a configuration diagram showing a configuration of a quantum state measurement apparatus (tomography apparatus) according to a first embodiment of the present invention. In the following, quantum state measurement of a four-dimensional time position single photon having four time positions where photons can exist and a fixed time position interval T will be described as an example.

  The quantum state measurement apparatus includes a 2-bit delay interferometer (first delay interferometer) 101, a 1-bit delay interferometer (second delay interferometer) 102, a photon detector 103, and a processing unit 104. The interferometer is, for example, a waveguide type optical interferometer.

  The 2-bit delay interferometer 101 is of the Mach-Zehnder type, and the delay time difference between two paths is 2T, and the phase difference between the two paths can be set to 0 or π / 2. A 4-bit time position single photon to be measured is input to the 2-bit delay interferometer 101.

  More specifically, the 2-bit delay interferometer 101 splits an input photon into two paths, a beam splitter 111, and a beam splitter 112 combines the light split into two paths and outputs the combined light to two output ports. And a delay unit 113 which gives a delay time of 2T to one of the lights separated by the beam splitter 111 and inputs the light to the beam splitter 112. The arm configured by the delay unit 113 includes a phase difference adjustment unit 114 that adjusts the phase difference between the two paths of light split by the beam splitter 111.

  The 1-bit delay interferometer 102 is of the Mach-Zehnder type, and the delay time difference between the two paths is T, and the phase difference between the two paths can be set to 0 or π / 2. Further, the input end of the 1-bit delay interferometer 102 is connected to one output end of the 2-bit delay interferometer 101.

  More specifically, the 1-bit delay interferometer 102 includes a beam splitter 121 that splits input photons into two paths, and a beam splitter 122 that combines the light split into two paths and outputs the combined light to two output ports. And a delay unit 123 for giving a delay time of T to one of the lights demultiplexed by the beam splitter 121 and inputting the delay time to the beam splitter 122. The arm configured by the delay unit 123 is provided with a phase difference adjustment unit 124 that adjusts the phase difference between the two paths of light split by the beam splitter 121.

  The photon detector 103 detects the arrival time of photons output from one output end of the 1-bit delay interferometer 102.

  The processing unit 104 sets the phase difference in the 2-bit delay interferometer 101 to 0 and the phase difference in the 2-bit delay interferometer 101 to π / 2 under the first measurement condition where the phase difference in the 1-bit delay interferometer 102 is 0. A second measurement condition in which the phase difference in the 1-bit delay interferometer 102 is 0, a third measurement in which the phase difference in the 2-bit delay interferometer 101 is 0 and the phase difference in the 1-bit delay interferometer 102 is π / 2 The arrival time of the photon detected by the photon detector 103 under the fourth measurement condition where the phase difference in the 2-bit delay interferometer 101 is π / 2 and the phase difference in the 1-bit delay interferometer 102 is π / 2 is Record for each measurement condition. Further, the processing unit 104 obtains the time position quantum state of the four-dimensional time position single photon, as will be described later, from the recorded information about the frequency of arrival time for each measurement condition.

  Since a four-dimensional time position single photon is input to the two-bit delay interferometer 101, six photons may be output from the two-bit delay interferometer 101 at different times. From 102, seven photons may be output at different times. The processing unit 104 records at which time of the seven possible time positions detected by the photon detector 103 the photon detector 103 detects a photon. Further, the processing unit 104 is not only the detection time of photons in the photon detector 103 but also phase difference information (first measurement condition, second measurement condition, third condition) to be supplied to the phase difference adjustment unit 114 and the phase difference adjustment unit 124. By also recording the measurement condition and the fourth measurement condition, the state of measurement corresponding to the photon detection time described later is recorded.

It is assumed that a state | i> in which a photon is present at time position i where 0 ≦ i ≦ 3 is input to the 2-bit delay interferometer 101. The input photons are branched into two paths by the beam splitter 111. Phase difference theta ₂ by time delay 2T and the phase difference adjustment unit 114 by the delay unit 113 at one of the routes branch is granted. In the beam splitter 112, photons passing through different paths are combined. Accordingly, among the output ports of the beam splitter 112, the output state at the port connected to the beam splitter 121 is given by the input / output relationship of the following equation.

  However, the state amplitude is normalized in consideration of energy storage with the output port of the other beam splitter 112 not connected to the beam splitter 121.

The relationship between input and output states in equation (12) is equivalent to multiplying the input state by the measurement operator Μ ₂ defined by the following equation from the left.

Therefore, the entering photons to 2-bit delay interferometer 101 is equivalent to performing a measurement by the measuring operator Micromax _2.

Similarly, the measurement operator Μ ₁ when photons are input to the 1-bit delay interferometer 102 can be defined by the following equation.

However, θ ₁ is the phase difference given by the phase difference adjustment unit 124.

The measurement that the photon detector 103 detects the arrival time of the photon corresponds to the projection measurement at seven time positions where the photon detector 103 can detect the photon. Therefore, photons input to the 2-bit delay interferometer 101 are detected if they are input to the subsequent 1-bit delay interferometer 102 and are further detected by the photon detector 103 at time j (0 ≦ j ≦ 6). The state of the photon is the state in which the measurement by the measurement operator 光子_w defined by the following equation is performed on the state of the input photon.

Therefore, when a single photon having the same time position quantum state ρ is repeatedly input to the 2-bit delay interferometer 101 N times, the expected value n ^p _{j of} the frequency with which the photon detector 103 detects photons at time _j is , “N ^p _j = NT _r (Μ ^j _w Μ ^{j †} _w ) = NT _r (ε ^j ))” (16) ”. Here, “ε ^j = Μ ^j _w Μ ^{j †} _w ”.

The operator ε ^j depends not only on the measurement time j in the photon detector 103 but also on the phase difference θ ₂ provided in the phase difference adjustment unit 114 and the phase difference θ ₁ provided in the phase difference adjustment unit 124. . Therefore, assuming that the phase difference θ ₂ and the phase difference θ ₁ are each in a state of taking 0 or π / 2, four combinations of phase differences (first measurement condition, second measurement condition, third measurement condition, fourth condition) A total of 28 ε ^j and the corresponding expected measurement frequency n ^p _j can be obtained from the combination of the measurement conditions) and the seven photon arrival times.

However, among these 28 types of measurements are included those making the same measurement. For example, when a photon is detected at time 0 in the photon detector 103, the measurement ε ⁰ is not based on the combination of the phase difference, and the projection measurement to the time position state | 0> in the state before being input to the beam splitter 111 Always correspond to The distinction between such states is as follows.

In order to indicate that the phase difference θ ₂ and the phase difference θ ₁ also depend, the above ε ^j is redefined as ε ^j, θ ₂ and θ ₁ again. Here, ε ^{j, θ 2, θ 1} use projection measurement operators P ^{j, θ 2, θ 1} for the input photon state, and “ε ^{j, θ 2, θ 1} = w ^{j, θ 2, θ 1} P ^{j, θ 2, θ 1.} (17) "can be written. However, w ^{j, θ2, θ1} is a real number representing the weight of the measurement frequency. Since w ^{j, θ 2 and θ 1} only represent weighting for the frequency of measurement, the essential difference in measurement is to compare whether the projection measurement operators P ^{j, θ 2 and θ 1} are different. This makes it possible to distinguish.

As a specific example, when (j, θ ₂ , θ ₁ ) = (0, 0, 0), (j, θ ₂ , θ ₁ ) = (0, 0, π / 2), (j, θ) A comparison is made in the case where ₂ , θ ₁ ) = (1, 0, 0). The projection measurement operators in these cases are respectively obtained by the above procedure as follows.

In this case, P ^0,0,0 and P ^{0,0, π / 2} are matrices in which all elements are equal, but P ^1,0,0 is different from the other two matrices. Therefore, in the case of (j, θ ₂ , θ ₁ ) = (0, 0, 0) and (0, 0, π / 2), it is considered that the same measurement is performed, and the obtained measurement frequencies are summarized However, (j, θ ₂ , θ ₁ ) = (1, 0, 0) is treated as another measurement.

By performing the comparison by this projection measurement operator for all (j, θ ₂ , θ ₁ ) cases, the quantum state measurement apparatus according to the first embodiment described above is compatible with 18 types of different measurements and this measurement. It can be seen that the frequency of

  There are 16 types of parameters for determining the state density function ρ in the four-dimensional case, so there are more types of measurement than types of parameters. Therefore, although these measurements include information that overlaps in an informational manner, by using the expected values of the measurement frequency corresponding to these measurement operators, equation (9), etc. Quantum state tomography can be performed.

In the conventional measurement, among photon measurement times j in the photon detector 103, only photon detection at j = 3 is used. Projection Measurements operator P ³ to distinguish this ^{measurement, .theta.2, .theta.1} is ^{"| Θ> θ2, θ1 = 1} /2 (| 0> + e iθ1 | 1> + e iθ2 | 2> + e i (θ1 + θ2 ⁾ | 3>) ... (21) ”becomes a projection measurement operator on ^{θ2 and θ1} .

theta _2, even changing the theta _1, the state | theta> ^{.theta.2, .theta.1} is always time position state | a i overlapping state of>. Therefore, other measurements necessary for quantum state tomography, such as measurements corresponding to the time position state | i> itself, can not be performed.

  In the present invention, the photon detector 103 can obtain more information at one time for input photons by utilizing the measurement results at different arrival times of photons. This enables high-dimensional quantum state tomography using a delay interferometer. In addition, when performing quantum state tomography, the type of change given to the measurement system is only the combination of the phase differences in the phase difference adjustment unit 114 and the phase difference adjustment unit 124, and four types of combinations of four dimensional time position quantum state quantum State tomography can be performed.

  As described above, according to the first embodiment, measurement can be performed with a simple configuration using a Mach-Zehnder type delay interferometer or the like, and quantum state tomography can be performed by more simple measurement. .

  By the way, in the above description it is assumed that all beam splitters used are perfect half beam splitters and there is no path dependent loss. However, in a real waveguide Mach-Zehnder interferometer, imperfections at these points often occur, and it may not be possible to reflect equation (13) completely.

On the other hand, the processing unit 104 corrects the frequency of arrival time based on the waveguide loss and the deviation of the branching ratio depending on the path in the delay interferometer, which is measured in advance, to obtain the time position quantum state. For example, equation (13) can be reflected. By measuring the path-dependent loss in advance, the measurement operator Μ ₂ of the 2-bit delay interferometer can be corrected as follows.

However, Δη ₂ is a real number indicating a path dependent loss. By performing the same correction on the measurement operator Μ ₁ of the 1-bit delay interferometer, it is possible to obtain a quantum state measurement apparatus capable of high-quality measurement even when there is a loss due to the path difference of the delay interferometer.

Second Embodiment
Second Embodiment Next, a second embodiment of the present invention will be described using FIG. FIG. 2 is a configuration diagram showing a configuration of a quantum state measurement device (tomography device) according to a second embodiment of the present invention. Also in the following, as in the first embodiment described above, quantum state measurement of a four-dimensional time position single photon having four time positions where photons can exist and a constant time position interval T will be described as an example.

  In the first embodiment described above, since the other of the beam splitter 112 and the output port of the beam splitter 122 is not used, fundamental photon loss occurs. On the other hand, in the second embodiment, in addition to the photon detector connected to one of the last stage delay interferometers connected in cascade, the delay interferometers subsequent to the delay interferometers other than the last stage are connected. It has a photon detector connected to the non-output terminal. More specifically, as shown in FIG. 2, the photon detector 131 is also connected to the other port of the beam splitter 112, and the photon detector 132 is also connected to the other port of the beam splitter 122.

  By doing this, it is possible to efficiently measure by eliminating the fundamental loss of photons. Also in these cases, by processing the measurement results of the photon detector 131 and the photon detector 132 in the processing unit 104 a in addition to the photon detector 103, quantum state measurement (quantum state tomography) as in the first embodiment. It can be performed. In the measurement operator used in the processing unit 104a, there is a distinguishable measurement operator which is not used in the case of the first embodiment, so that information on the input quantum state can be obtained more than simple correction of loss. Can.

Third Embodiment
Next, a third embodiment of the present invention will be described with reference to FIG. FIG. 3 is a configuration diagram showing a configuration of a quantum state measurement apparatus (tomography apparatus) according to a third embodiment of the present invention. The following describes quantum state measurement of d-dimensional time position n photons with d time positions each having n photons available and a constant time position interval T.

  The first embodiment and the second embodiment described above are directed to a four-dimensional time position single photon, but when there are n photons, n devices shown in the first and second embodiments are connected in parallel. It may be used as it is. In addition, when the dimension of one photon is larger than 4, it is possible to cope with the case of an arbitrary dimension d by increasing the number of delay interferometers cascade-connected in multiple stages. In the following, a quantum state measurement apparatus in the case where two-photon and eight-dimensional time position photons are targeted will be described. It is assumed that two photons can be distinguished by each light wavelength.

First, the quantum state measuring apparatus according to the third embodiment includes an optical demultiplexer 301 which inputs a two-photon eight-dimensional time position photon and outputs two photons to different output ports. Also, two multistage interferometers 302a and 302b are provided, each of which comprises three types of Mach-Zehnder delay interferometers connected in cascade to the output ports of the optical demultiplexer 301. When the time position photon has d time positions (d dimension), the multistage interferometer is configured of a Mach-Zehnder type delay interferometer of K type (K is a minimum integer larger than log ₂ d).

  In addition, the quantum state measuring apparatus according to the third embodiment is connected to each of two multistage interferometers 302a and 302b, and the photons output from one output end of the multistage interferometer 302a and the multistage interferometer 302b. And two photon detectors 303 a and photon detectors 303 b for detecting the arrival time of Further, the processing unit 304 is provided to record arrival times of photons detected by the photon detector 303a and the photon detector 303b.

Here, the K types of delay interferometers constituting each of the multistage interferometers 302a and 302b have 2 ^k T (0 ≦ k ≦ K−1) in which the delay time difference between the two paths is different. There is. In addition, the K types of delay interferometers constituting each of the multistage interferometers 302a and 302b can set the phase difference between the two paths to 0 or π / 2.

More specifically, the multistage interferometer 302a has a 4-bit delay interferometer 305a having a 4T propagation time difference and adjustment means of the phase difference θ _3a between two paths, and a 2T propagation time difference between the two paths. and 2-bit delay interferometer 306a having adjusting means of the phase difference theta _2a, and a 1-bit delay interferometer 307a having a regulating means of the propagation time difference and phase difference theta _1a of T between the two paths.

Also, the multistage interferometer 302b has a 4-bit delay interferometer 305b having a means for adjusting the propagation time difference of 4T and the phase difference θ _3b between the two paths, and a propagation time difference and phase difference θ of 2T between the two paths. A 2-bit delay interferometer 306b having _2b adjustment means and a 1-bit delay interferometer 307b having adjustment means for T propagation time difference and phase difference θ _1b between two paths. The phase difference in each delay interferometer can be individually set to a value of 0 or π / 2.

In addition, the processing unit 304 sets the maximum K2 ^K + (K + 1) d types of temporally different detection signals and the respective delay interferometers for each photon detected by each photon detector 303a and photon detector 303b. From the measurement of a plurality of measurement conditions by the combination of 2 ^K phases by the phase difference of 0 or π / 2, the arrival times of 2 ^Kn {K 2 ^K + (K + 1) d} ⁿ types of signals are measured for each measurement condition From the information about the frequency of arrival time for each measurement condition recorded and recorded, the time position quantum state of the two-photon eight-dimensional time position photon is determined as described later.

  In the third embodiment configured as described above, the measurement result of the photon detector 303a corresponds to the measurement of the state related to the photon A, and the measurement result of the photon detector 303b corresponds to the measurement of the state related to the photon B. By considering combined simultaneous measurements, we can perform quantum state tomography for the two-photon state.

  Further, compared with the first embodiment and the second embodiment, the photon detector 303a and the photon detector 303b can detect photons by adding the 4-bit delay interferometer 305a and the 4-bit delay interferometer 305b. The kind of time with sex increases. Also, by increasing the combinations of phases that can be taken by each delay interferometer, it becomes possible to obtain measurement results more than the types of measurements required for quantum state tomography in the case of eight dimensions. Thus, eight-dimensional quantum state tomography can be performed. As a result of these, it is possible to perform high-dimensional quantum state tomography in the case of two-photon eight-dimensional case.

In the third embodiment, a combination of a phase difference provided multistage interferometer 302a, the multi-stage interferometer 302b photons A, for each photon B is 8 patterns each, the measurement setup 64 ² ways which was necessary in the prior art Can be achieved with 8 ² setups.

  As described above, in the present invention, Mach-Zehnder delay interferometers are cascaded in multiple stages, and in each delay interferometer, the phase difference between the two paths can be set to 0 or π / 2, The arrival time of photons output from the delay interferometer of the final stage is recorded for each measurement condition with a phase difference of 0 or π / 2, and the information on the frequency of the arrival time for each measurement condition recorded indicates the time position photon I made it to obtain the time position quantum state. As a result, according to the present invention, it is possible to reduce the error and deterioration of the measurement result and to measure the quantum state more easily.

  The present invention is not limited to the embodiments described above, and many modifications and combinations can be made by those skilled in the art within the technical concept of the present invention. It is clear.

  101: 2-bit delay interferometer (first delay interferometer) 102: 1-bit delay interferometer (second delay interferometer) 103: photon detector 104: processing unit 111, 112: beam splitter 113: Delay unit 114 phase difference adjustment unit 121, 122 beam splitter 123 delay unit 124 phase difference adjustment unit

Claims (4)

A quantum state measurement device for measuring the time position quantum state of a four-dimensional time position single photon having four time positions where photons can exist and a constant time position interval T,
A delay time difference between two paths is 2T, a phase difference between the two paths can be set to 0 or π / 2, and a four-dimensional time position single photon is input. 1 delay interferometer,
The input end is connected to one output end of the first delay interferometer to be cascaded, and the delay time difference between two paths is T, and the phase difference between the two paths is 0 or π. And a second Mach-Zehnder delay interferometer that can be set to
A photon detector for detecting arrival time of photons output from one output end of the second delay interferometer;
The arrival time of the photon detected by the photon detector under the first measurement condition where the phase difference in the first delay interferometer is 0 and the phase difference in the second delay interferometer is 0,
The arrival time of the photon detected by the photon detector under the second measurement condition where the phase difference in the first delay interferometer is π / 2 and the phase difference in the second delay interferometer is 0,
The arrival time of the photon detected by the photon detector under the third measurement condition where the phase difference in the first delay interferometer is 0 and the phase difference in the second delay interferometer is π / 2,
The phase difference in the first delay interferometer is π / 2, and the phase difference in the second delay interferometer is π / 2. The arrival time of the photon detected by the photon detector under the fourth measurement condition is measured. And a processing unit for recording for each condition and obtaining the time position quantum state of the four-dimensional time position single photon from the information on the frequency of arrival time for each measurement condition recorded. A quantum state measurement apparatus for measuring the time position quantum states of d-dimensional time position n photons having d time positions at which n photons can each be present and a constant time position interval T,
An optical demultiplexer that inputs the d-dimensional time position n photons and outputs n photons to different output ports;
N multistage interferometers comprising K type (K is a minimum integer larger than log ₂ d) Mach-Zehnder type delay interferometers cascade-connected to the output port of each of the optical splitters;
n photon detectors connected to each of the n multistage interferometers to detect arrival times of photons output from one output end of the multistage interferometers;
A processing unit that records arrival times of photons detected by the photon detector;
The K types of delay interferometers constituting each of the multistage interferometers have 2 ^k T (0 ≦ k ≦ K−1), each having a different delay time difference between the two paths,
The K types of delay interferometers constituting each of the multistage interferometers are configured such that the phase difference between the two paths can be set to 0 or π / 2,
The processing unit sets up to K2 ^K + (K + 1) d temporally different detection signals for each photon detected by each of the photon detectors and 0 or π / set in each of the delay interferometers. Measured by recording the arrival times of 2 ^Kn {K2 ^K + (K + 1) d} ⁿ kinds of signals for each measurement condition from measurement of a plurality of measurement conditions by combination of 2 ^K kinds of phases by phase difference of 2 A quantum state measuring device, wherein a time position quantum state of the d-dimensional time position n photon is obtained from information on frequency of arrival time for each condition. In the quantum state measuring device according to claim 1 or 2,
In addition to the photon detector connected to one of the delay interferometers of the last stage connected in cascade,
What is claimed is: 1. A quantum state measuring device comprising a photon detector connected to an output end to which a delay interferometer of a stage subsequent to the delay interferometer other than the final stage is not connected. In the quantum state measuring device according to any one of claims 1 to 3,
The processing unit determines the time position quantum state by correcting the frequency of arrival time based on the waveguide loss and deviation of the branching ratio depending on the path in the delay interferometer, which is measured in advance. Quantum state measuring device to be.

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