JP4996290B2 - Time-entangled photon pair measurement device - Google Patents

Description

  The present invention relates to a time-entangled photon pair measuring apparatus for evaluating the quality of a time-entangled photon pair having a quantum mechanical correlation with respect to two time positions where a photon may exist.

  In recent years, new types of communication systems using quantum mechanics such as quantum cryptography and quantum teleportation have been proposed. Quantum cryptography is a technique for transmitting cipher private key information by making "0" and "1" correspond to quantum states such as polarization and phase of individual photons, and divides one photon further. This is an encryption method that performs key distribution in the common key cryptosystem using the fact that it is generally not possible to observe physical quantities without changing the quantum state, and the quantum state of the photon is changed by observation. This is an extremely secure cryptographic communication system in which the security of the cryptographic key is guaranteed by the principle of quantum mechanics, in which traces of eavesdropping remain. Quantum teleportation is a system for transferring a quantum state, and is used for extending the transmission distance in the quantum cryptography and for signal transfer in a quantum information processing apparatus such as a quantum computer.

  A photon pair (quantum entangled photon pair) having a quantum mechanical correlation is an important element in the quantum information communication system as described above. For example, a quantum cryptography system suitable for long-distance transmission can be realized by using a entangled photon pair. Moreover, in order to transfer the quantum state of a photon by the quantum teleportation, it is necessary to share a entangled photon pair between a transmitter and a receiver.

  In order to apply the entangled photon pair to the communication system as described above, it is necessary to prepare a high-quality entangled photon pair. Therefore, it is important to evaluate the quality of the entangled photon pair. One of the evaluation methods is to measure the density matrix of photon pairs. Regarding a entangled state related to the polarization state of a photon pair (polarized entangled photon pair), a method for measuring a density matrix of a photon pair, called quantum state tomography, has already been proposed in Non-Patent Document 1.

The polarization entangled photon pair will be described below. | H> indicates the state of a single photon having horizontal (horizontal) polarization (H polarization), and | V indicates the state of a single photon having vertical (vertical) polarization (V polarization). > One of the photon pairs in the polarization entangled state is referred to as a signal photon (signal photon), and the other is referred to as an idler photon. At this time, the state (| Φ _p >) of the polarization entangled photon pair is expressed by the following equation (1), for example.

It is assumed that the signal idler photon pair is separated and sent to two persons A (for example, Alice) and B (for example, Bob) which are separated from each other, and both perform polarization measurement on each photon. According to the meaning of equation (1), if A observes H-polarization | H>, B always observes | H> with respect to the photon paired with it. Similarly, if A observes V-polarized light | V>, B always observes | V> for photons paired therewith. In addition, Equation (1) uses the basis of the HV polarization, but this is a basis using another basis, for example, a clockwise circular polarization | R> and a counterclockwise circular polarization | L>. Even if rewritten, the correlation with respect to the polarization of two photons is maintained.

  In a polarization entangled photon pair, it is assumed that the quantum state of a photon is expressed as a superposition of two polarization modes. In general, a pure single photon having an arbitrary polarization is expressed by the following equation (2).

Here, φ is a phase having a value from 0 to 2π. Such a quantum state relating to the polarization of a photon can be expressed as a point on the surface of the Poincare sphere, which is a display method of the polarization state of light. A quantum state relating to the polarization of a photon is shown in the Poincare sphere format in FIG. Here, located on the equator of the sphere ^{| D +>, | D -} > Each

Represents. In addition, | L>, | R>

It corresponds to.

In the quantum state tomography disclosed in Non-Patent Document 1, after separating two photons in a polarization entangled state, for each photon, a quarter of the Poincare sphere (through the center of the sphere, 2 points corresponding to the midpoint of the arc connecting the two points of the intersection of the two planes and the surface of the sphere, and a piece of the sphere divided into four parts by two planes orthogonal to each other) The projection measurement to the polarization state corresponding to a total of four points is performed (in FIG. 1, for example, this corresponds to the projection measurement to the four states of states | H>, | V> | L>, | D ⁺ >). The above four projection measurements are applied to individual photons to determine the number of events in which two photons are detected simultaneously. That is, simultaneous counting is performed using a total of 16 combinations of projection measurements for two photons. By processing the 16 measurement results obtained in this way by the method described in Non-Patent Document 1, a density matrix represented by a 4 × 4 matrix of polarization entangled photon pairs can be constructed. .

  Non-Patent Document 1 also shows a method for projective measurement of a polarization state. The outline is described below. FIG. 2 shows a projection measurement system in the polarization state. This projection measurement system has a rotatable quarter wave plate (QWP) 21, a rotatable half wave plate (HWP) 22, and a transmission axis set to a vertical (V) polarization. And a photon detector 24 that receives an output photon from the polarizer 23. The rotation matrix T (θ) of the angle θ is expressed by the following equation.

When the fast axis is fixed in the H polarization direction, the Jones matrix of HWP22 and QWP21 is

It can be expressed as. The Jones matrices of QWP21 and HWP22 in which the fast axis rotates the angles θ _q and θ _h counterclockwise from the H direction are expressed by the following equations (3) and (4), respectively.
H (θ _h ) = T (θ _h ) hT (−θ _h ) (3)
Q (θ _q ) = T (θ _q ) qT (−θ _q ) (4)

In the projection measurement system shown in FIG. 2, it is assumed that the rotation angles of QWP 21 and HWP 22 are set to θ _q and θ _h , respectively, and photons are detected by photon detector 24. At this time, it means that the input photon is projected to the state | x> shown by the following equation (5).
| x> = Q (θ _q ) ⁻¹ H (θ _h ) ⁻¹ | V> (5)

According to the equation (5), for example, if (θ _q , θ _h ) is set to (0, 0), projection measurement for the state | V> can be performed, and (θ _q , θ _h ) is changed to (0, π / 4), the projection measurement for the state | H> can be performed.

Daniel. F. V. James, et. Al., “Measurement of qubits”, Physical Review A, vol. 64, pp. 052312-1 to -5 (2001).

  As an entangled photon pair relating to a physical quantity different from the above-mentioned polarization entangled photon pair, there is a time-position entangled photon pair (a photon state entangled with respect to the time position, with the time position of the photon as an observation amount). If | k> is a state where there is one photon at the time position k, an example of the time-position entangled photon pair is expressed by the following equation (6).

Here, the subscripts s and i indicate a signal photon and an idler photon, respectively. This type of quantum entanglement is based on the fact that an arbitrary quantum state related to the time position is expressed by the following equation (7).

Here, φ is a phase having a value from 0 to 2π.

As in the case based on the polarization, the quantum state related to the time position represented by the above equation (6) is also replaced by | H> → | 1> · | V> → | 2> in FIG. It can be represented by a point on the sphere (FIG. 3). At this time, | L>, | R>, | D ⁺ >, and | D ⁻ > are superpositions of states | 1> and | 2> as shown in the following equation.

On the Poincare sphere in the quantum state with respect to this time position, the same four-point projection measurement as in the case of polarization is performed for each photon, and the coincidence rate based on a total of 16 projection measurement combinations is measured. A two-photon density matrix can be constructed using the same method as in Non-Patent Document 1. However, clearly, the projection measurement method (FIG. 2) of the polarization state described in the previous section (Background Art) is not applicable to the projection measurement of the quantum state with respect to the time position. As described above, in the prior art, since the method of projective measurement of the quantum state related to the time position is unknown, the quantum tomography for the time position entangled photon pair has not been performed.

  The present invention has been made in view of such problems, and an object of the present invention is to provide a time-position entangled photon pair measuring apparatus that enables quantum state tomography of time-position entangled photon pairs and enables accurate evaluation of tangled quality. Is to provide.

In order to achieve the above object, the present invention provides a time-position entangled photon pair measuring device for measuring the quantum state of a entangled photon pair with respect to two time positions separated by a predetermined time interval, wherein each pair of photon pairs An optical branching unit that splits the light input to the photon into two paths, an optical coupler having a 2 × 2 input / output terminal, and two paths of light branched by the optical branching unit Delay means for inputting light to one input terminal of the optical coupler in a state where the light is delayed by the predetermined time interval with respect to the light on the other path, and a phase difference between the two paths of light branched by the optical branching means A delay interferometer having a phase difference adjusting means for adjusting the photon, a photon output from the delay interferometer and a photon detector for detecting the arrival time thereof, and a pair of quantum entangled photons for two time positions The light When the photon pair is detected and detected by the photon detector, the photon detector detects the photon pair at which of the three time positions where the photon is detected. And for each photon of the entangled photon pair with respect to the two time positions, the first time position, the third time position, and the phase difference of the delay interferometer among the three time positions When the photon count is set to two values different from each other by π / 2, photon counting of four projection states at each of the second time positions is performed, and 16 combinations of four projection states at the same time are calculated simultaneously. Counting is performed .

  The photon detector may be connected to one of the two output terminals of the optical coupler or to both of them.

  With the above configuration, the present invention enables quantum state tomography of entangled photon pairs in time position, and enables accurate evaluation of entangled quality.

(First embodiment)
As a first embodiment of the present invention, a time-position entangled photon pair measuring apparatus when one photon detector is used for each photon will be described.

  A delay interferometer as shown in FIG. 4 is used for the projection measurement of the quantum state with respect to the time position. The delay interferometer 41 has a propagation time difference equal to the time interval between two time position modes constituting a quantum state in two paths. It also has a mechanism for adjusting the phase difference of light propagating through the two paths. Further, in the present embodiment, a case is considered where the photon detector 47 is connected to only one output port of the delay interferometer 41.

  The delay interferometer 41 will be described in detail. The delay interferometer 41 has an optical branching unit 42 for branching light input to each photon forming a photon pair into two paths, and a 2 × 2 input / output terminal. The optical coupler 43 and a delay means for causing the light of one path branched by the optical branching means 42 to be input to one input terminal of the optical coupler 43 in a state where the light is delayed to the other path by a predetermined time interval. 1 and a 1-bit delay Mach-Zehnder interferometer having a phase difference adjusting unit 45 that adjusts a phase difference between two paths of light branched by the optical branching unit 42.

  A photon detector 46 is connected to only one output terminal (one output port) of the optical coupler 42, and this photon detector 46 detects a photon output from the optical coupler 42 and its arrival time. The information processing device 48 records where in each of the three time positions that the photon detector 46 may detect each photon that forms a entangled photon pair for the two time positions. As will be described in detail later, the information processing device 48 uses the first time position, the third time position, and the delay interferometer among the three time positions for each photon of the photon pair. When the phase difference of 41 is set to two values different by π / 2, photon counting is performed in four ways at each of the second time positions, and 16 ways are obtained according to the four ways of projection of two photons. Simultaneously count the combinations.

  When a quantum state configured in two time position modes is input to the delay interferometer 41 configured as described above, photons may be observed at three time positions in the output of the delay interferometer 41. In the following, since the measurement at the time positions 1 and 3 can determine whether the state of the input photon is | 1> or | 2>, the measurement at the time base (time base time base) The measurement at the second time position is called the measurement in the energy base (energy base). The photon detection based on the energy base means that the input state is projected into a superposition state of | 1> and | 2>. It is only probabilistic that it will be detected whether the photon is detected in the time base or energy base in the measurement.

  In the second time slot, the phase of the first pulse is rotated by changing θ, and it is considered that the state combined with the second pulse is output. So if a photon is detected in this second time slot,

Can be thought of as being projected. In the above equation (8), if θ = 0 and a photon is detected in the second time slot, the projection measurement is performed to the state | D ⁺ >. In the above equation (8), θ = −π If the photon is detected in the second time slot when / 2, the projection measurement to the state | L> is performed.

  If a photon is detected in the first time slot, it indicates that the input photon state is always | 1>. Therefore, it can be considered that the projection measurement to the state | 1> has been performed. . Similarly, if it is detected in the third slot, it indicates that the input photon state is always | 2>, so it can be considered that the projection measurement to state | 2> has been performed. However, it should be noted that the time base measurement has half the probability (1 / √2 in terms of probability amplitude) as compared with the energy base as described below.

If a photon of | D ⁺ > is input to the delay interferometer 41 with θ = 0 and measured on an energy basis (if there is no system loss and the photon is output on the energy base), 100 Photons are detected with a probability of%. That is, the photons are always output from the port connected to the photon detector 47 out of the two outputs of the delay interferometer 41.

  On the other hand, it is assumed that the photon of | 1> is input to the delay interferometer 41 and measured on the time base. At this time, since the photons are output from the two output ports of the delay interferometer 41 with an equal probability, even if there is no loss of the system and the photons are output to the time base, the probability that the photons are detected is 50%. . In other words, time base measurements can be thought of as projecting photons to | 1> / √2 or | 2> / √2.

Based on the above, for example, four measurements of | 1>, | 2>, | D ⁺ >, and | L> are performed for each photon. If the density matrix is displayed with | 1> and | 2> as the base, the state | Ψ _ν > after the projection of two photons is (| 11>, | 12>, | 21>, | 22>).
It is expressed by a vector having four components. Here, ν is a number from 1 to 16 indicating a combination of projection states of two photons. These 16 projection states are shown in Table 1.

Here, the coincidence rate obtained for the projection state combination ν in the experiment is m _ν, and in the above time-based projection measurement, half of the photons are output to another port. Assuming that the coincidence rate corrected in this way is n _v , the relationship between n _v and m _v is expressed by the following equation (9).
n _v = αm _v (9)

  Here, α is 1 when both photons are measured on an energy basis, 2 when only one time base is measured, and 4 when both time bases are on (see Table 1).

By using n _ν (ν = 1-16) obtained in this measurement and performing the same processing as the above equation (1), a density matrix of time-entangled photon pairs can be constructed.

(Second Embodiment)
Next, as a second embodiment of the present invention, a time-position entangled photon pair measuring apparatus when two photon detectors are used for each photon will be described.

In the first embodiment, half of the photons are output from the other port of the delay interferometer 41 during measurement in the time base, and therefore correction of the coincidence rate data by the above equation (9) is necessary. It was. Therefore, in the present embodiment, as shown in FIG. 5, the photon detectors 46 and 47 are arranged at the two output ports of the respective delay interferometers 41, and the two-photon detectors 46 and 47 are used in the time base measurement. The information processing device 48 takes the simultaneous count of either one of the above and the detection result of the other photon. The energy-based measurement is the same as in the first embodiment. If the quantum efficiencies of the two photon detectors 46 and 47 are the same, the coincidence rate n _v can be obtained without correction by the above equation (9).

(Other embodiments)
In the above, the preferred embodiment of the present invention has been described by way of example. However, the embodiment of the present invention is not limited to the above-described example, and is within the scope of the claims. Various modifications such as replacement, change, addition, increase / decrease in the number of components, change in shape design, etc. are all included in the embodiment of the present invention. In addition, the present invention may be applied to a system composed of a plurality of devices, or may be applied to an apparatus composed of one device.

It is a conceptual diagram which shows the Poincare sphere display of the quantum state based on polarization. It is a block diagram which shows the structural example of the conventional apparatus which performs the projection measurement of the quantum state based on a polarization. It is a conceptual diagram which shows the Poincare sphere display of the quantum state based on a time position. It is a block diagram which shows the structure of the time position entangled photon pair measuring apparatus which performs the projection measurement of the quantum state based on the time position using the delay interferometer in the 1st Embodiment of this invention. It is a block diagram which shows the structure of the time position entangled photon pair measuring apparatus in the 2nd Embodiment of this invention.

Explanation of symbols

41 Delay Interferometer (1 Bid Delay Mach-Zehnder Interferometer)
42 branching means 43 optical coupler 44 delay means 45 phase difference adjusting means 46, 47 photon detector 48 information processing apparatus

Claims (2)

A time-entangled photon pair measuring device for measuring the quantum state of a quantum entangled photon pair with respect to two time positions separated by a predetermined time interval;
Optical branching means for branching the light input to each photon forming a photon pair into two paths, an optical coupler having 2 × 2 input / output terminals, and two paths of light branched by the optical branching means , A delay means for inputting the light of one path to one input terminal of the optical coupler in a state delayed by the predetermined time interval with respect to the light in the other path, and 2 branched by the optical branching means A delay interferometer having phase difference adjusting means for adjusting the phase difference of light in the path;
A photon output from the delay interferometer and a photon detector for detecting its arrival time;
When a pair of quantum entangled photons relating to two time positions is input to the optical branching means and output from the optical coupler and detected by the photon detector, each photon forming the photon pair is detected. Record where it was detected at three possible time locations ,
For each photon of the entangled photon pair with respect to the two time positions, the phase difference between the first time position, the third time position, and the delay interferometer among the three time positions is π / 2. Perform four-way photon counting at each of the second time positions when set to two different values, and perform 16-way combination counting by four-photon four-projection states. Time position entangled photon pair measuring device. A time-entangled photon pair measuring device for measuring the quantum state of a quantum entangled photon pair with respect to two time positions separated by a predetermined time interval;
Optical branching means for branching the light input to each photon forming a photon pair into two paths, an optical coupler having 2 × 2 input / output terminals, and two paths of light branched by the optical branching means , A delay means for inputting the light of one path to one input terminal of the optical coupler in a state delayed by the predetermined time interval with respect to the light in the other path, and 2 branched by the optical branching means A delay interferometer having phase difference adjusting means for adjusting the phase difference of light in the path;
A photon detector connected to one or both of the two output terminals of the optical coupler and connected to both, and a photon detector for detecting the arrival time of the photon output from the delay interferometer;
When a pair of quantum entangled photons relating to two time positions is input to the optical branching means and output from the optical coupler and detected by the photon detector, each photon forming the photon pair is detected. Record where it was detected at three possible time locations,
For each photon of the entangled photon pair with respect to the two time positions, the phase difference between the first time position, the third time position, and the delay interferometer among the three time positions is π / 2. Perform four-way photon counting at each of the second time positions when set to two different values, and perform 16-way combination counting by four-photon four-projection states. Time position entangled photon pair measuring device.

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