Parallel preparation method of multi-body entangled states among distributed nodes

Abstract

The invention discloses a parallel preparation method of a multi-body entangled state among distributed nodes, which comprises the following steps of: placing N quantum memories in a distributed manner, arranging an optical switch in front of each static bit in a scene in which M static bits are stored in each memory, performing joint coding on high-dimensional single photons and the optical switches, and obtaining a multi-body entangled state of each quantum memory; when a single photon passes through the quantum memories, only a specific static bit interacts with the single photon, and then the single photon sequentially passes through the N quantum memories to obtain hybrid entanglement of a photon state and a plurality of quantum bits. And then generalized X-base measurement is carried out on the single photon, so that the hybrid entangled state collapses on a certain Fourier base of the single photon, and finally preparation of a many-to-many entangled state between distributed nodes is realized. According to the method, efficient preparation of many-to-many entangled states among distributed nodes is realized by utilizing a high-dimensional time coding single photon, and the requirement on coherence time of a quantum memory in an entanglement preparation process is reduced.

Description

Technical Field

[0001] The present invention belongs to the field of quantum information, and particularly relates to a method for parallel preparation of multi-body entangled states between distributed nodes. Background Art

[0002] Quantum entanglement is the core resource for constructing quantum networks. The non-local property of quantum entanglement allows quantum states to be shared among different particles, making it possible for technologies such as classical-communication connection and distributed sensing to be transcended. A distributed quantum network needs to simultaneously operate multiple pairs of quantum information processing nodes with entangled states distributed at different locations. Among them, distributed quantum entanglement is the basis for constructing large-scale quantum networks. For a long time, scientists have been committed to how to efficiently establish quantum entanglement between distant nodes. Given that photons have the characteristics of being convenient to detect, easy to operate, and not easily coupled with the environment, and have the natural advantage of fast propagation speed, they are the primary choice as entanglement mediators. However, photons will decay exponentially as the transmission distance increases during fiber-optic transmission. Therefore, in the preparation of long-distance distributed quantum entangled states, photons face serious channel loss problems, and the loss of photon resources severely restricts the practical application of distributed quantum entanglement.

[0003] In order to overcome the photon attenuation caused by too long distances, when preparing quantum entanglement between distant nodes, the common method is to cut the long distance into the sum of multiple short distances. With the help of quantum repeaters and multiple pairs of entangled photon pairs, entanglement between multiple short-distance nodes is first achieved, and then entanglement purification technology is used to share high-fidelity entangled states between adjacent nodes. Then, entanglement swapping is used to establish entanglement between non-adjacent nodes, and finally, quantum entanglement between two distant nodes is realized. Since photons from different entanglement sources do not arrive at the relay station simultaneously, in order to effectively complete entanglement swapping, this method not only involves entanglement purification and entanglement swapping technologies, but also requires the use of a quantum memory as a caching tool at the relay station to let the first-arriving qubits wait for the later-arriving qubits. However, as the distance between nodes increases, the physical resources used in the above method will increase rapidly, and the complicated intermediate processes will also bring a greater probability of errors, resulting in a significant reduction in the efficiency of entangled state preparation.

[0004] In order to prepare an entangled state between two non-local nodes, a single photon first interacts with a stationary qubit at one of the nodes, and then this single photon either interacts with a single photon that has already been entangled with a qubit inside another node, or directly interacts with a qubit inside another node, thereby establishing entanglement between two distant nodes. Currently, the schemes for simultaneously generating multiple pairs of entangled states are mainly based on the protocol for generating a single pair of qubit entanglement.

[0005] In 2010, Togan et al. achieved quantum entanglement between the polarization of a single photon and the spin of a single electron in a diamond nitrogen-vacancy (NV) center. In 2013, Bernien et al.'s NV center experiment achieved quantum entanglement between distant electron spins. A series of conditional projection and reflection methods based on NV centers made it possible to realize the interaction between a single photon and multiple NV centers. In 2019, Piparo et al. proposed an entanglement preparation scheme for preparing two pairs of two-body entangled states by sequentially passing a single encoded photon through four NV centers. Zhou Hui, Xie Zhihao et al. further optimized the scheme on this basis and proposed a scheme that can generate multiple pairs of entangled states simultaneously, and even achieve the simultaneous generation of multiple pairs of multi-body entangled states. In 2022, Zheng et al. proposed an entanglement scheme that can realize any pair of Bell states by using high-dimensional time-bin encoding of single photons.

[0006] The above methods not only require a large amount of single-photon resources, but also, since the success or failure of the preparation of each pair of entangled states is independent of each other, the multi-pair entangled state preparation scheme based on the single-pair qubit entanglement protocol also faces the problem that the already prepared entangled pairs need to wait for the successful preparation of other entangled pairs that have not been completed yet. The waiting time will be jointly determined by the distance between nodes, the number of target entangled pairs, and the probability of successfully generating a single pair of entangled states, which poses high requirements on the coherence time of qubits and the coherent storage time of quantum memories. Summary of the Invention

[0007] The purpose of the present invention is to provide a method for parallel preparation of multi-body entangled states between distributed nodes, which solves the problems of low utilization rate of single-photon resources and high requirements for the coherence time of quantum memories in the parallel preparation of distributed multi-body entangled states by encoding high-dimensional single photons, and improves the preparation efficiency of entangled states.

[0008] The technical solution for achieving the purpose of the present invention is as follows:

[0009] A method for parallel preparation of multi-body entangled states between distributed nodes, including: distributing N quantum memories, each memory storing a scenario of M stationary qubits, and a light switch is arranged in front of each stationary qubit; first, by jointly encoding single photons and light switches, when a single photon passes through the quantum memory, only specific stationary qubits will interact with the single photon, and then let the single photon sequentially pass through N quantum memories to obtain the hybrid entanglement of the photon state and multiple qubits, and then perform a generalized X-basis measurement on the single photon to collapse the hybrid entangled state on a certain Fourier basis of the single photon, and finally realize the preparation of multiple pairs of multi-body entangled states between distributed nodes.

[0010] Further, the joint encoding of single photons and optical switches includes: converting the time slice information carried by a single photon into an M-bit binary number (l) D =(i M-1 ,…,i m ,…,i 1 ,i 0 ) B , i m ∈{0,1}, and the optical switch OS state before the m-th qubit in the memory corresponds to i m in the binary number.

[0011] Further, the state of the single photon is a superposition state of d-dimensional time slices, where the dimension d is a parameter related only to the logarithm M of the generated entangled state, and d = 2 M .

[0012] Further, l indicates that the single photon may appear in the l-th time slice, and l ∈ {0, 1…d - 1}

[0013] Further, the optical switch OS encoding rules in each quantum memory are the same, so that when the photon states passing through the quantum memory are the same, the states of the qubits in the N memories are the same.

[0014] Further, performing a generalized X-basis measurement on a single photon to cause the hybrid entangled state to collapse on a certain Fourier basis of the single photon specifically includes: the Fourier transform of the photon state is expressed as ω = 2πi / d, and successfully detecting a single photon in any k basis will indicate that the system collapses to Integrating to obtain

[0015] Compared with the prior art, the significant advantages of the present invention are as follows:

[0016] (1) The present invention realizes the parallel preparation of multi-body entangled states between distant nodes only by using a single high-dimensional encoded photon, exponentially reducing the limitation of the single photon on the preparation efficiency of multi-pair multi-body entangled states due to transmission channel loss;

[0017] (2) The present invention realizes the preparation of multi-pair entangled states only with a single photon, eliminating the waiting problem of the previously successfully prepared entangled pairs in the multi-pair entangled state preparation scheme based on the single-pair entangled state preparation protocol, saving quantum resources such as photons, time, and space required in the entangled state preparation process, and reducing the requirements for the coherence duration of qubits and quantum memories;

[0018] (3) In this solution, the dimension d of the high-dimensional single photon is a parameter related only to the target entanglement logarithm, and the increase in the number of entangled nodes will not lead to an increase in the requirement for the dimension of the single photon. Description of the Drawings

[0019] Figure 1 Schematic diagram of the optical path for a specific embodiment of the present invention. Specific implementation manner

[0020] In order to make the purpose, technical solution and advantages of the present application clearer, the following will give a more detailed description of the specific steps of the present solution. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0021] This embodiment proposes a method for parallel preparation of multi-body entangled states between distributed nodes, which involves a method for parallel preparation of multi-body entangled states between distributed nodes by using a single photon encoded in a high-dimensional space interacting with multiple static qubits, including the following steps:

[0022] Step 1, convert the time-bin (Time-bin Qudit) information carried by the single photon into an M-bit binary number, (l) D =(i M-1 …i 1 i 0 ), i B ∈{0,1}; the state of the single photon is a superposition state of d-dimensional time bins, and the dimension d is a parameter related only to the number of pairs M of the generated entangled states, where d = 2 m ^M. The l represents that the single photon may appear in the l-th time bin, l ∈ {0,1…d-1} M ^M.

[0023] Step 2, place an optical switch (OS) in front of each qubit of each memory to control whether the single photon interacts with the qubit; the memories are distributed, and each memory stores M stationary bits. The state of the optical switch OS in front of each bit is closely related to the state of the single photon in Step 1. Specifically, the binary number (i M-1 …i 1 i 0 ) B corresponds to the state of the optical switch OS in front of the m-th qubit in the memory; m and the state of the optical switch OS in front of the m-th qubit in the memory;

[0024] Step 3, the photon passes through N quantum memories in sequence to obtain a hybrid entangled state of the photon and MN stationary bits; for the N quantum memories, the optical switch OS encoding rules in each quantum memory are the same, so that when the states of the photons passing through the quantum memories are the same, the states of the qubits in the N memories are the same;

[0025] Step 4: Perform a generalized X - basis measurement on the single photon after it passes through the last quantum memory. Convert the hybrid entanglement formed by the photon and the MN stationary qubits into multi - body entanglement between the qubits at the same positions in multiple pairs of N distributed quantum memories.

[0026] The principle and verification of the method of the present invention are as follows.

[0027] Reference Figure 1 , is the optical path schematic diagram of the present invention. The figure includes N nodes distributed over a long distance, with position encodings of 0, 1…N - 1. Each node stores M qubits, and the position encodings of the qubits are 0, 1…M - 1. There is an encoded optical switch in front of each qubit. The single photon with high - dimensional encoding passes through N nodes in sequence and selectively interacts with the qubits in the nodes through the optical switch. After the photon interacts with the qubit at the last node, a generalized X - basis measurement is performed on the single photon. Successfully detecting the photon on any Fourier basis indicates the successful preparation of the entangled state. The principles of each link can be described as follows:

[0028] (1) First, assume that the initial states of all stationary qubits are |0>. When a photon interacts with it, the qubit state flips to |1>. Further assume that the probability of the single photon appearing in each time slice is the same. Then the single - photon state At the same time, assume that when the single - photon state is |D〉, after interacting with the qubits of N nodes, the states of all qubits are expressed as According to the encoding rule (l) D =(i M-1 …i 1 i 0 ) B , i m ∈{0,1}. We assume that when i m = 1, the optical switch is in the reflection mode, the photon can interact with the qubit and flip the qubit state. Otherwise, the optical switch is in the transmission mode, the photon does not interact with the qubit associated with this optical switch, and the qubit state remains unchanged. Thus, after the photon |D> passes through the first node, the system state can be described as At this time

[0029] (2) The photon passes through N nodes in sequence. The encoding rules of the optical switches in each node are the same. So, after interacting with the qubits of N nodes, the state of the system is At this time Combined with the photon state |φ>, at this time the entire system is in a superposition state

[0030] (3) After the photon completes the interaction with the last node, perform a generalized X-basis measurement on the photon. After the Fourier transform of the photon state, the successful measurement of the photon in any Fourier basis state indicates the successful preparation of the multi-body entangled state of multiple pairs of qubits encoded at the same positions of N distributed nodes. The Fourier transform of the photon state can be expressed as ω = 2πi / d, and the successful detection of a single photon in any k basis will indicate that the system collapses to Integrating them can obtain Therefore, if there is a photon response during the generalized X-basis measurement, the preparation of the entangled state is successful.

[0031] In summary, the present invention uses a single photon with a high-dimensional encoding and an encoded optical switch, and performs a generalized X-basis measurement on the single photon after the photon sequentially passes through the quantum memories at N nodes, thereby realizing the parallel preparation of the multi-body entangled state between the distributed nodes.

[0032] The present invention can use a single photon with a high-dimensional time encoding to efficiently prepare the multi-pair multi-body entangled state between distributed nodes, greatly reducing the interference caused by the transmission loss of single photons when constructing a large-scale quantum network. At the same time, it greatly saves the quantum resources such as single photons, time, and space required in the entanglement preparation process, and reduces the requirements for the coherence time of the quantum memory during the entanglement preparation process.

[0033] The above describes the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the above embodiments and the descriptions in the specification only illustrate the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention will have various changes and improvements, and these changes and improvements all fall within the scope of the present invention claimed.

Claims

1. A method for parallel preparation of multi-body entangled states between distributed nodes, characterized in that: include: N quantum memories are placed in a distributed manner, each of which stores M static bits, and an optical switch is set in front of each static bit. First, the single photon and the optical switch are jointly encoded so that only specific static bits will interact with the single photon when the single photon passes through the quantum memory. Then, the single photon is passed through the N quantum memories in sequence to obtain the hybrid entanglement of the photon state and multiple quantum bits. Then, a generalized X-basis measurement is performed on the single photon so that the hybrid entangled state collapses on a certain Fourier basis of the single photon, finally realizing the preparation of many-to-many entangled states between distributed nodes.

2. The method for parallel preparation of multi-body entangled states between distributed nodes according to claim 1, characterized in that: The joint encoding of the single photon and the optical switch includes: converting the time slice information carried by the single photon into an M-bit binary number (1) D =(i M-1 ,…,i m ,…,i1,i0) B ,i m ∈{0,1}, the OS state of the optical switch before the mth quantum bit in the memory is the same as the binary number i m Corresponding.

3. The method for parallel preparation of multi-body entangled states between distributed nodes according to claim 2, characterized in that: The state of the single photon is a superposition state of d-dimensional time slices, where the dimension d is a parameter related only to the logarithm M of the generated entangled state, where d=2 M .

4. The method for parallel preparation of multi-body entangled states between distributed nodes according to claim 3, characterized in that: The l indicates that a single photon may appear in the lth time slice, l∈{0,1…d-1}.

5. The method for parallel preparation of multi-body entangled states between distributed nodes according to claim 1, characterized in that: The optical switch OS encoding rules in each quantum memory are the same, so that when the state of the photons passing through the quantum memory is the same, the states of the quantum bits in the N memories are the same.

6. The method for parallel preparation of multi-body entangled states between distributed nodes according to claim 3, characterized in that: Performing generalized X-basis measurement on a single photon causes the hybrid entangled state to collapse on a certain Fourier basis of the single photon. Specifically, the Fourier transform of the photon state is expressed as Successful detection of a single photon in any k basis would indicate that the system has collapsed to Integration

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