Composite entanglement purification method based on measurement

Abstract

The invention discloses a quantum composite entanglement purification method based on measurement, which comprises the following steps: an entanglement source prepares two pairs of same composite entanglement states and respectively sends discrete and continuous parts to a user information sender and an information receiver, and the information sender and the information receiver respectively locally prepares discrete and continuous GHZ states. The information sender inputs the two pairs of discrete parts of the entangled state and the two modes of the continuous GHZ state into the two polarization beam splitters, and the information receiver inputs the two modes of the continuous part and the continuous GHZ state into the inlets of the two beam splitters respectively; measuring an output port of the beam splitter by the two parties, recording a space of a discrete part, and comparing measurement results through classical communication; the entangled state is reserved if the measurement results are all even space, otherwise, the entangled state is discarded. The method provided by the invention can be expanded to a composite entanglement state of any number of users.

Description

Technical Field

[0001] The invention belongs to the technical field of quantum communication, and in particular relates to a composite entanglement purification method. Background Art

[0002] Quantum communication refers to the transmission of information using the basic principles of quantum mechanics. Quantum entanglement is an important resource for quantum communication. In recent years, composite entangled states have also been widely used in the field of quantum communication, such as quantum secure direct communication, quantum key distribution, quantum relay, quantum secret sharing, etc. However, the quality of the entangled state will be reduced due to the influence of environmental noise in the experiment. In order to solve this problem, researchers have developed a quantum entanglement purification method (EPP), which can extract some entangled systems with high entanglement from the ensemble of mixed entangled states with low entanglement, thereby improving the efficiency and security of quantum communication methods. EPP usually requires 2 copies of exactly the same entangled state as materials in each round of purification operation, and then the users who share the entangled pair perform bilateral operations respectively, and finally measure and compare the results through classical communication. If the comparison result meets the requirements, it is successful and the entanglement is retained, otherwise it is discarded. The two successfully retained entangled states can be purified in the next round to further improve the entanglement.

[0003] Most of the existing EPPs focus on discrete variable (DV) entanglement, only a few continuous variable (CV) EPPs have been proposed, and even fewer composite entanglement purification methods (HEPPs) that combine CV and DV. In 2013, Sheng et al. first proposed a HEPP, in which the composite entangled state used was composed of polarized single photons and coherent states. It is a quantum composite entanglement resource with broad research and application prospects. On the other hand, measurement-based EPP (MBEPP) is a new type of EPP that has the potential to become an important component of measurement-based quantum relays. Unlike traditional gate-based EPPs, MBEPP does not require complex quantum gate operations, but uses measurements to complete purification, which is easier to implement and more noise-robust.

[0004] In view of this, it is necessary to design a measurement-based composite entanglement purification method. Summary of the invention

[0005] The purpose of the present invention is to use a lower quality composite entangled state as a raw material for entanglement purification to obtain a higher quality composite entangled state.

[0006] To achieve the above objectives, the present invention provides a composite entanglement purification method, comprising the following steps:

[0007] Step 1: The user information sender and the information receiver share two pairs of identical composite entangled states |φ distributed by the entanglement source through the noisy quantum channel + > abThe information sender holds the discrete (DV) part A, which is a polarized photon state, and the information receiver holds the continuous (CV) part B, which is a coherent state. In addition, the information sender and the information receiver prepare discrete GHZ states locally. D > and continuous GHZ state |GHZ C >.

[0008] Step 2: The information sender inputs the DV part of the two pairs of entangled states into the two spatial modes a1 and a2 of the device Md mainly composed of a polarization beam splitter (PBS), and inputs the two modes of its GHZ state into the other two spatial modes d1 and d2 of Md. The information receiver inputs the CV part of the two pairs of entangled states into the two spatial modes b1 and b2 of the device Mc mainly composed of a beam splitter (BS), and inputs the two modes of its GHZ state into the other two spatial modes c1 and c2 of Mc.

[0009] Step 3: The information sender uses 4 photon detectors (PD) to perform polarization parity measurement on the output ports of the two PBSs and records the parity of the two discrete parts. The information receiver uses 4 PDs to perform coherent state parity measurement on the output ports of the two BSs and records the parity of the two continuous parts.

[0010] Step 4: The information sender and the information receiver compare the parity of their measurement results through classical communication.

[0011] Step 5: Determine whether the purification is successful based on the measurement results of both parties. The ideal situation is that all the parity measurements of the information sender and the information receiver are even parity. If the comparison results meet the ideal situation, the entangled state is retained, otherwise it is discarded. The 2 pairs of retained entangled states can be used for the next round of purification cycle.

[0012] In addition, if the initial state is a phase flip error, we can convert it into a bit flip error using the Hadamard operation and then use this protocol to purify it in the next step.

[0013] The present invention adopts the above technical solution, which has the following effects compared with the prior art:

[0014] 1. The entangled state purified by the present invention combines the advantages of polarization photon entanglement and coherent state entanglement, and can be used to construct quantum composite entangled networks in the future.

[0015] 2. The present invention does not require complex quantum gate operations, but uses measurement to complete purification, which is easier to implement and has stronger noise robustness.

[0016] 3. The method proposed in the present invention can be extended to the composite entangled state of any number of users. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1It is a flow chart of a composite entanglement purification method provided by the present invention.

[0018] Figure 2 This is an experimental method based on the composite entanglement purification method provided by the present invention, in which the purple square represents a discrete quantum bit, the blue circle represents a continuous quantum bit, BS and PBS represent a 50:50 beam splitter and a polarization beam splitter, respectively. D1 to D8 at the end of the path represent photon detectors. DETAILED DESCRIPTION

[0019] In order to make the purpose, technical methods and advantages of the present invention more clear, the present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0020] It should be emphasized that in the process of describing the present invention, various formulas and constraints are distinguished by consistent labels, but the use of different labels to mark the same formula and / or constraints is not excluded. The purpose of this setting is to more clearly illustrate the characteristics of the present invention.

[0021] Please refer to Figure 1 to Figure 2 As shown, a preferred embodiment of the present invention provides a measurement-based composite entanglement purification method (MBHEPP), which includes the following process:

[0022] First, the information sender Alice and the information receiver Bob share two pairs of identical composite entangled states |φ distributed by the entanglement source through a noisy channel. + > ab The information sender holds the discrete (DV) part a, which is the polarized photon state, and the information receiver holds the continuous (CV) part b, which is the coherent state. The composite entangled state generated by the entanglement source |φ + > ab is one of the following four orthogonal Bell states, and has the following form:

[0023]

[0024] |H> and |V> represent polarized photon states (horizontally polarized and vertically polarized), which are the DV part of the composite entanglement; |±α> represents the coherent state, which is the CV part of the composite entanglement. + > ab After being distributed to the information sender and the information receiver through the noisy channel, there is a probability (1-F) that a bit flip occurs, thus becoming a mixed state ρ ab =F|φ + > ab <φ + |+(1-F)|ψ + > ab < +|, where F>0.5. The two-copy mixed state held by the information sender and the information receiver is denoted as ρ a1b1 and ρ a2b2 , so the initial system can be written as This system can be expressed as a probabilistic superposition of four composite entangled pure states: as well as The probabilities are F 2 , (1-F) 2 , F(1-F) and (1-F)F.

[0025] The main components of the device Md for the DV part of the information sender inputting two pairs of entangled states are two photon detectors and a PBS (transmitting horizontally polarized photons and reflecting vertically polarized photons). The main components of the device Mc for the CV part of the information receiver inputting two pairs of entangled states are two photon detectors and a 50:50 BS (functioning as ). Specifically, Md and Mc can implement the parity check of the DV part and the CV part respectively as follows:

[0026]

[0027] Here|1 d > and |0 d > represents the odd and even values ​​of the DV partial parity measurement results, and |1 c > and |0 c > represents the odd and even values ​​of the CV backup parity measurement results.

[0028] The information sender and the information receiver use their own devices to operate and measure the received photons and the resource states they generate. 1 The evolution of the four items after passing through these devices are:

[0029]

[0030]

[0031]

[0032]

[0033] The information sender and the information receiver compare the parity measurement results of both parties through two-way classical communication.

[0034] The success of purification is determined based on the parity measurement results of both parties. The ideal situation is that the parity measurement results of both the information sender and the information receiver are even parity. If the comparison result does not meet the ideal situation, the entangled state is discarded. If it meets the ideal situation, the output of path d3 and path c3 is retained. Therefore, the information sender and the information receiver use F2 The probability of getting Or (1-F) 2 The probability of getting Therefore, the information sender and the information receiver obtain a new mixed state ρ d3c3 =F 1 |φ + > d3c3 <φ + |+(1-F 1 )|ψ + > d3c3 < + |.

[0035] Its fidelity F 1 for

[0036]

[0037] The probability of successful purification is If the initial state satisfies Then we can get the fidelity F 1 >F.

[0038] In addition, if the initial state is a phase flip error, we can convert it into a bit flip error using the Hadamard operation and then use this protocol to purify it in the next step.

[0039] From the above method description, we can see that only the first and fourth terms will have the final successfully retained state, and the two cross terms in the middle will be discarded because neither of the cross terms will satisfy the parity of the ideal measurement result.

[0040] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that include computer-usable program code.

[0041] The above embodiments are only used to illustrate the technical method of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical method of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical method of the present invention.

Claims

1. A measurement-based composite entanglement purification method, characterized in that The steps include: Step 1: The information sender and the information receiver share two pairs of identical composite entangled states |φ distributed by the entanglement source through the noisy quantum channel + > ab The sender of the information holds the discrete part A, which is the polarized photon state; the receiver of the information holds the continuous part B, which is the coherent state; In addition, the information sender and the information receiver prepare discrete GHZ states locally respectively. D > and continuous GHZ state |GHZ C > Step 2: The information sender inputs the discrete parts of the two pairs of entangled states into the two spatial modes a1 and a2 of the device Md composed of the polarization beam splitter, and inputs the two modes of the GHZ state of the information sender into the other two spatial modes d1 and d2 of Md; the information receiver inputs the continuous parts of the two pairs of entangled states into the two spatial modes b1 and b2 of the device Mc mainly composed of the beam splitter, and inputs the two modes of the GHZ state of the information receiver into the other two spatial modes c1 and c2 of Mc; Step 3: The information sender uses 4 photon detectors to perform polarization parity measurement on the output ports of the two polarization beam splitters and records the parity of the two discrete parts. The information receiver uses 4 photon detectors to perform coherent state parity measurement on the output ports of the two beam splitters and records the parity of the two continuous parts. Step 4: The information sender and the information receiver compare the parity of their measurement results through classical communication; Step 5: Determine whether the purification is successful based on the measurement results of both parties; the ideal situation is that all parity measurement results of the information sender and the information receiver are even parity; if the comparison result meets the ideal situation, the entangled state is retained, otherwise it is discarded; 2. Perform the next round of purification cycle on the retained entangled state.

2. The measurement-based composite entanglement purification method according to claim 1, characterized in that: In step 1, the composite entangled state |φ generated by the entanglement source + > ab is one of the following four composite Bell states, in the form |H> and |V> represent polarized photon states, which are the discrete parts of the composite entanglement; |±α> represents the coherent state, which is the continuous part of the composite entanglement; the composite entangled state |φ is generated. + > ab After being distributed to the information sender and the information receiver through the noisy channel, there is a probability (1-F) that a bit flip occurs, thus becoming a mixed state ρ ab =F|φ + > ab <φ + |+(1-F)|ψ + > ab < + |, where F>0.5; The two-copy mixed state held by the information sender and the information receiver is denoted as ρ a1b1 and ρ a2b2 , so the initial system is written as It can be expressed as a probabilistic superposition of four composite entangled pure states: as well as The probabilities are F 2 , (1-F) 2 , F(1-F) and (1-F)F.

3. The measurement-based composite entanglement purification method according to claim 2, characterized in that: The main components of the device Md used by the information sender to input the discrete parts of two pairs of entangled states are two photon detectors and a polarization beam splitter; the main components of the device Mc used by the information receiver to input the continuous parts of two pairs of entangled states are two photon detectors and a 50:50 beam splitter; specifically, the device Md and the device Mc respectively implement the parity check of the discrete part and the continuous part as follows: Here|1 d > and |0 d > represents the odd and even values ​​of the discrete partial parity measurements, and |1 c > and |0 c > represents the odd and even values ​​of the continuous backup parity measurement results.

4. The measurement-based composite entanglement purification method according to claim 3, characterized in that: The information sender and the information receiver use their own devices to operate and measure the received photons and the resource states they generate. The evolution of the four items of ρ1 after passing through these devices is:

5. The measurement-based composite entanglement purification method according to claim 4, characterized in that: The information sender and the information receiver compare the parity measurement results of both parties through two-way classical communication.

6. The measurement-based composite entanglement purification method according to claim 5, characterized in that: The success of purification is determined based on the parity measurement results of both parties. The ideal situation is that all parity measurement results of the information sender and the information receiver are even parity. If the comparison result does not meet the ideal situation, the entangled state is discarded. If it meets the ideal situation, the output of path d3 and path c3 is retained. When purification is successful, the information sender and the information receiver use F 2 The probability of getting Or (1-F) 2 The probability of getting Therefore, the information sender and the information receiver obtain a new mixed ρ d3c3 =F1|φ + > d3c3 <φ + |+(1-F1)|ψ + > d3c3 < + |; Its fidelity F1 is The probability of successful purification is If the initial state satisfies The fidelity F1>F is obtained; in addition, if a phase flip error occurs in the initial state, it is converted into a bit flip error using the Hadamard operation, and then purified in the next step using this protocol.

Images