^{1}State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing, China^{2}School of Science, Beijing University of Posts and Telecommunications, Beijing, China^{3}School of Information and Communication Engineering, Beijing University of Posts and Telecommunications, Beijing, China^{4}School of Electronic Engineering, Beijing University of Posts and Telecommunications, Beijing, China^{5}Beijing Key Laboratory of Space-ground Interconnection and Convergence, Beijing University of Posts and Telecommunications, Beijing, China

Quantum information networks can transmit quantum states and perform quantum operations between different quantum network nodes, which are essential for various applications of quantum information technology in the future. In this paper, a potentially practical scheme for implementing nonlocal quantum controlled-not (CNOT) gate operations on quantum-dot-confined electron spins between two quantum network nodes is presented. The scheme can realize parallel teleportation of two nonlocal quantum CNOT gates simultaneously by employing hyperentangled photon pairs to establish quantum channel, which can effectively improve the channel capacity and operational speed. The core of the scheme are two kinds of photon-spin hybrid quantum CNOT gate working in a failure-heralded and fidelity-robust fashion. With the heralded mechanism, the nonlocal CNOT gates can be implementated with unity fidelities in principle, even if the particularly ideal conditions commonly used in other schemes are not satisfied strictly. Our analysis and calculations indicate that the scheme can be demonstrated efficiently (with efficiency exceeding 99%) with current or near-future technologies. Moreover, the utilized photon-spin hybrid quantum gates can be regarded as universal modules for many other quantum information processing (QIP) tasks. Therefore, the scheme is potential for constructing elementary quantum networks, and realizing nolocal QIP with high channel capacities, high fidelities, and high efficiencies.

## 1 Introduction

Quantum information technology, which aims to develop new theories and methods for processing information based on the laws of quantum mechanics, has developed very rapidly during the past decades. The main branches of this field, i.e., quantum communication [1], quantum computation [2–4], and quantum metrology [5, 6], have been established and become the focus of research. One of the ultimate directions for the development and integration of quantum information technology in the future is to construct quantum information networks [7–9], which are considered as spatially separated quantum network nodes connected by quantum communication channels. The fundamental characteristic of quantum networks lies in the capability to nonlocally transmit not only quantum states but also quantum operations between different quantum nodes, which makes it essential for various applications such as quantum secure direct communication [10–15] and secure multi-party quantum computation [16–21]. The quantum network can therefore significantly improve the power of quantum information processing (QIP) compared with individual QIP systems.

For the physical implementation of quantum networks, photon is the best carrier for fast and reliable communication over long distance, which plays the central role in the realization of nonlocal interactions between spatially distant quantum network nodes [22–24]. In particular, some interesting schemes for implementing nonlocal quantum operations between two different nodes have been proposed based on the sharing of entangled photon pairs, which act as the quantum channel for the teleportation of quantum gates [25–29]. In contrast to other schemes which rely on the transmission of a single photon through an optical channel to transmit interaction between two separate nodes, an attractive advantage of teleportation-based architectures is that the environmental noise and photon loss could be well overcome *via* entanglement purification together with quantum repeaters [30–36]. Moreover, photon possesses multiple degrees of freedom (DOFs) for encoding, such as polarization, spatial mode, frequency, time bin, and orbit angular momentum. Photon hyperentanglement [37–39], which refers to entanglements simultaneously existing in multiple DOFs of photons, has been demonstrated and proven useful in high-performance quantum communications [40–45], and hence represents a valuable quantum resource for quantum networks.

Solid-state spin systems such as electron or hole spins confined in semiconductor quantum dots (QDs) are ideal candidates for stationary qubits due to their good properties such as spin coherence and potential scalability [46–50]. Fast initialization, manipulation, and measurement of electron spins in charged QDs have been well-investigated [51–54]. Spin echo and dynamical decoupling techniques can be used to preserve the electron-spin coherence [55, 56]. With the help of optical microcavities or nanocavities, effective coupling between photons and singly charged QDs can be realized in coupled QD-cavity systems, which is crucial for realizing various quantum interfaces between single photons and spins [57–60]. With the photon-spin quantum interfaces, many QIP schemes such as universal quantum logic gates [61–67], quantum entanglement generation and analysis [68–73], and quantum entanglement purification and concentration [74–77] have been proposed. The QD-cavity systems supply ideal platforms for implementing quantum networks by constituting the quantum nodes and providing photon-spin interfaces [78, 79]. Significant progress has been achieved towards the practical demonstration of the photon-spin interfaces. For example, photon sorter [80], photon switch [81], Faraday rotation induced by a single electron or hole spin [82, 83] have been explored in experiments. These experiments were performed in the weakly-coupled cavity quantum electrodynamics (QED) regime.

In this work, we present a potentially practical scheme for implementing nonlocal quantum controlled-not (CNOT) gate operations on QD-confined electron spins between two quantum network nodes, by exploiting optical microcavities, hyperentangled photon pairs, and linear-optical elements. The scheme can realize parallel teleportation of two nonlocal quantum CNOT gates simultaneously by employing hyperentangled photon pairs to establish quantum channel, which can effectively improve the channel capacity and operational speed of the quantum network. The core units of the scheme are two kinds of photon-spin hybrid quantum CNOT gate constructed based on the interaction between an input photon and a singly charged QD mediated by a single-sided optical microcavity, which work in a failure-heralded and fidelity-robust fashion. With the help of the heralded mechanism, the nonlocal CNOT gates can be implemented with unity fidelities in principle, even if the particularly ideal conditions commonly used in other schemes are not satisfied strictly. Our analysis and calculations indicate that the scheme can be demonstrated efficiently with current or near-future technologies. Moreover, the photon-spin hybrid quantum gates used in this scheme can be regarded as universal modules, and can be used in many other QIP tasks. Therefore, the scheme has potential application prospects in constructing elementary quantum networks and realizing nonlocal QIP tasks with high channel capacities, high fidelities, and high efficiencies.

## 2 Interaction between an input photon and a singly charged QD mediated by a single-sided optical microcavity

As shown in Figure 1A, we consider a singly charged semiconductor QD [e.g., a self-assembled In(Ga)As QD or a GaAs interface QD] with an excess electron embedded in a single-sided optical micropillar cavity constructed by two GaAs/Al(Ga)As distributed Bragg reflectors (DBRs) and with a circular cross-section. The bottom DBR is 100% reflective and the top DBR is partially reflective so that the single-sided cavity hypothesis is valid. When we consider an input single photon interacting with the singly charged QD mediated by the single-sided optical microcavity, it has been proven that the optical property of the singly charged QD is dominated by the spin-dependent optical transitions of a negatively charged exciton (*X*^{−}). The *X*^{−} is composed of two electrons bound to one hole, and the optical transition rule is based on the Pauli exclusion principle and the conservation of total spin angular momentum. The related energy levels and the optical transition rule of *X*^{−} transitions is shown in Figure 1B. The left-circularly polarized photon |*L*⟩ and the right-circularly polarized photon |*R*⟩ drive the transitions |*↑*⟩ → |*↑↓⇑*⟩ and |*↓*⟩ → |*↓↑⇓*⟩, respectively. Here, we use ∣ *↑*⟩ and ∣ *↓*⟩ to represent the excess-electron spin states with spins *⇑*⟩ and ∣ *⇓*⟩ represent the heavy-hole spin states with spins *z*-axis) is along the normal direction of the cavity.

**FIGURE 1**. **(A)** Schematic diagram of a singly charged QD inside a single-sided optical micropillar cavity with two DBRs and circular cross section. *g* is the QD-microcavity coupling strength. *γ* is the exciton decay rate. *κ* and *κ*_{s} are the cavity-mode decay rates into the input-output mode and the leaky mode (side leakage), respectively. **(B)** The energy levels and the optical transition rule of exciton transitions. |*L*⟩ and |*R*⟩ represent the photonic left-circularly and right-circularly polarized states, respectively. The left-circularly polarized photon |*L*⟩ and the right-circularly polarized photon |*R*⟩ drive the transitions |*↑*⟩ → |*↑↓⇑*⟩ and |*↓*⟩ → |*↓↑⇓*⟩, respectively. *z* axis is the spin-quantization axis.

By solving the Heisenberg-Langevin equations of the cavity mode operator *X*^{−} dipole operator

Here, *ω*_{c}, *ω*, and *X*^{−} transition, respectively. *κ* and *κ*_{s} are the input-output decay rate and the leakage rate of the cavity field mode. *g* is the coupling strength between *X*^{−} and the cavity mode. *γ* is the *X*^{−} dipole decay rate.

Here we set *g* = 0), the reflection coefficient is

When the excess electron is in the spin state ∣ *↑*⟩(∣ *↓*⟩), only the |*L*⟩(|*R*⟩) state photon can couple to the transition |*↑*⟩↔|*↑↓⇑*⟩(|*↓*⟩↔|*↓↑⇓*⟩) and obtain the reflection coefficient *r* (Δ, *g*), while the |*R*⟩(|*L*⟩) photon would feel an empty cavity and obtain the reflection coefficient *r* (Δ, 0). This is due to the optical transition rule and the cavity-QED effect. The reflection coefficients of coupled case *r* (*Δ*, *g*) and uncoupled case *r* (*Δ*, 0) can be significantly different, which is the so called giant circular birefringence effect [57]. As the single-photon input-output process is coherent, this description holds for superposition states as well. Therefore, when a horizontal polarized photon

Here, *r*_{±}(Δ) = [*r* (Δ, 0)±*r* (Δ, *g*)]/2, *p*_{1} = [|*r* (Δ, 0)|^{2} + |*r* (Δ, *g*)|^{2}]/2 is the probability of the photon being reflected by the QD-cavity system. That is, after the photon interacts with the QD-cavity system, the photon-spin system evolves into an orthogonally entangled state with two components: 1) due to the imperfect photon scattering process in reality, both the photon and electron spin remain unchanged with the probability of |*r*_{+}(Δ)|^{2}/*p*_{1}; 2) both the photon and electron spin are flipped with the probability of |*r*_{−}(Δ)|^{2}/*p*_{1}, which is the valid interaction we use to construct the quantum gates between a single photon and an electron spin. We note that the evolution rule is general and does not depend on the particularly ideal conditions [*κ*_{s} → 0, *g* > (*κ*, *γ*), |Δ|≪ *g*] usually used in other schemes.

## 3 Heralded photon-spin hybrid quantum CNOT gates with theoretically unity fidelities

Now we present two hybrid quantum CNOT gates, which are represented by *r*_{−}(Δ) and reflection coefficient _{i} (*i* = 1, 2, 3, 4) represents a single-photon detector. DL is the delay line, which makes the photon components in spatial modes s_{1} and s_{2} arrive the output port simultaneously without affecting the quantum state. PBS_{j} (*j* = 1, 2, … , 6) is a polarization beam splitter, which transmits the photonic horizontal polarization component |*H*⟩ and reflects the vertical polarization component |*V*⟩. _{t} (*t* = 1, 2, 3) is a half-wave plate which performs a polarization bit-flip operation _{f} (*f* = 1, 2) completes the polarization rotation *u* and *d* are to distinguish two different spatial modes in the quantum circuits. The red dots denote the optical switches.

**FIGURE 2**. Schematics of the heralded photon-spin hybrid CNOT gates. **(A)** The spatial mode of the photon is the control qubit, and the QD-confined electron spin is the target qubit. **(B)** The polarization of the photon is the control qubit, and the QD-confined electron spin is the target qubit. All the functions of the optical elements are presented in the text.

As shown in Figure 2A, suppose the initial states of the input photon and the electron spin confined in QD are |*ψ*_{p}⟩ = (*k*|*H*⟩ + *l*|*V*⟩) (*m*|*s*_{1}⟩ + *n*|*s*_{2}⟩) and |*ψ*_{e}⟩ = *μ*| + ⟩ + *ν*| − ⟩, respectively. Before the photon enters the

Here, s_{1} and s_{2} are two spatial modes of the photon, respectively. When the photon enters the unit from the input port, the photon component in spatial mode s_{1} passes through the delay line DL with state unchanged. The photon component in spatial mode s_{2} passes PBS_{1}, and the |*H*⟩(|*V*⟩) photon component interacts with the QD-cavity system *via* spatial mode *u*(*d*) as described by Eq. 4. Then the photon component in spatial mode *u* passes *P*_{θ} and X_{1}, the photon component in spatial mode *d* passes X_{1}. After which, the state of the photon-spin system becomes

where the subscripts *u* and *d* are used to distinguish the spatial modes. Then, the photon components pass through VBS and PBS_{2}, respectively. When neither of the photon detectors D_{1} and D_{2} click, we call this a valid state evolution, and we get the state

Then the heralded photon-spin hybrid CNOT gate is completed, where the spatial mode of the incident photon is the control qubit and the electron spin confined in the QD is the target qubit. The polarization state of the photon does not change after this process.

On the contrary, if the photon detector D_{1} or D_{2} clicks, these two cases mean that errors occur in the state evolution. Any detector response means photon loss, and we get an invalid quantum state evolution result. This failure-herald mechanism guarantees the fidelity of the

The *ψ*_{0}⟩. Similar to the *ψ*_{0}⟩ to

The hybrid CNOT gate _{1} or D_{2} clicks, the operation failed, and the spin state does not change. We can repeat the operation until success.

These two hybrid CNOT gates

## 4 Nonlocal high-fidelity quantum controlled-not gates on QD-confined electron spins between quantum network nodes

In this section, we propose the scheme for nonlocal high-fidelity quantum CNOT gates between two remote quantum network nodes Alice and Bob, resorting to single-sided QD-cavity systems, hyperentangled photon pairs, and linear optical elements. As shown in Figure 3, the quantum network node consists of two electron spins confined in QD-cavity systems. We assume the QD-cavity systems in the scheme are identical. Network node Alice holds the electron spins *AA*′ and the initial state is |Ψ_{AA′}⟩ = (*α*| +⟩ +*β*|−⟩)_{A} (*α*′| +⟩ +*β*′|−⟩)_{A′}. Network node Bob holds the electron spins *BB*′ and the initial state is |Ψ_{BB′}⟩ = (*γ*| +⟩ +*ξ*|−⟩)_{B} (*γ*′| +⟩ +*ξ*′|−⟩)_{B′}. The subscripts *A*, *A*′, *B*, and *B*′ are used to distinguish the four electron spins. The coefficients satisfy the relation |*α*|^{2} + |*β*|^{2} = 1, |*α*′|^{2} + |*β*′|^{2} = 1, |*γ*|^{2} + |*ξ*|^{2} = 1, and |*γ*′|^{2} + |*ξ*′|^{2} = 1. The electron spin *A* (*A*′) of Alice is the control qubit, while the electron spin *B*(*B*′) of Bob is the target qubit. The hyperentangled photon pair *a* and *b* are used to build the quantum channel and encoded in two DOFs, i.e., the polarization and the spatial mode. Photons *a* and *b* are initially prepared in the state *a* and *b* are used to distinguish two photons. |*a*_{1}⟩(|*b*_{1}⟩) and |*a*_{2}⟩(|*b*_{2}⟩) are the two spatial modes of photon *a*(*b*), respectively. The scheme is detailed as follows.

**FIGURE 3**. Schematic of nonlocal high-fidelity quantum CNOT gates between remote quantum network nodes. The electron spin *A* (*A*′) of Alice is the control qubit, while the electron spin *B*(*B*′) of Bob is the target qubit. *a* and *b* are hyperentangled photon pair. BS_{i} (*i* = 1, 2, 3) is a 50:50 beam splitter used to perform a Hadamard operation on the spatial mode DOF of a photon, which completes the following transformation: _{j} (*j* = 1, 2, … , 6) represents a half-wave plate to perform a Hadamard operation on the polarization of a photon, which completes the following transformation: _{1}-D_{4} and D_{5}-D_{8}. The other elements have the same function as that in Figure 2.

Before the photons enter the circuits, the state of the system composed of photon *a*, photon *b*, electron spin *AA*′ and *BB*′ is

After the hyperentangled photon pair *a* and *b* are prepared, photon *a* is sent to Alice, while photon *b* is sent to Bob simultaneously. Photon *a* enters the node Alice and sequentially passes through H_{1}, H_{2}, _{3}, H_{4}, BS_{1}, _{2} in both spatial modes *a*_{1} and *a*_{2}. If none of the photon detectors in the _{0} to |Ψ⟩_{1} in unnormalized form

At the same time, photon *b* enters the node Bob and sequentially passes through *b*_{1} and *b*_{2}. If no detector in the

Then, Hadamard operations are performed on photon *b* in both the polarization and the spatial mode *via* H_{5}, H_{6}, and BS_{3}. Before photon *b* gets the photon detectors D_{5}-D_{8}, the state of the system is

Finally, the photons *a* and *b* pass the PBSs and get the local photon detectors D_{1}-D_{4} and D_{5}-D_{8}, respectively. Alice and Bob communicate their measurement results through a classical communication channel. According to the results, Alice and Bob choose the corresponding single-qubit rotation operations on electron spins according to Table 1. For example, if the photon pair *ab* are finally detected in the state |*a*_{1}*b*_{1}*H*_{a}*H*_{b}⟩, the state of the four-spin system *AA*′*BB*′ is

**TABLE 1**. The measurement results of the photons and the corresponding single-qubit gate rotation operations required on the electron spins.

which means two CNOT gates between the spins *AA*′ of Alice and the spins *BB*′ of Bob have been implemented. If the photons are detected in the state |*a*_{1}*b*_{2}*V*_{a}*V*_{b}⟩, Alice should perform a *σ*_{z} operation on the electron spin *A* and a − *σ*_{z} operation on the spin *A*′, and Bob should perform a *σ*_{x} operation on the spin *B*′. After the operations above, the state |Ψ_{AA′BB′}⟩ can be obtained. Other situations can be seen in Table 1. Moreover, if any photon detector in the *via* launching a new pair of hyperentangled photons.

So far, we have described the teleportation of two nonlocal CNOT gates operations on spin qubits between two quantum network nodes in parallel assisted by single-sided QD-cavity systems. Electron spin *A* (*A*′) of Alice is the control qubit, while the electron spin *B*(*B*′) of Bob is the target qubit. Two CNOT gates are achieved simultaneously. The modular functional units make the circuit more flexible and extensible. For instance, if we let the electron spin *A* (*A*′) of Alice control *B*′(*B*) of Bob, we only need to let photon *b* pass through a linear optical

**FIGURE 4**. Schematic of the

## 5 Discussion and summary

In this section, we discuss the performance of the scheme, which can be characterized by fidelity and efficiency. We define the fidelity as *F* = |⟨Ψ_{r}|Ψ_{i}⟩|^{2}, where |Ψ_{r}⟩ is the final state of the system composed of four electron spins hold by two network nodes Alice and Bob in reality, and |Ψ_{i}⟩ is the final state of the system in ideal conditions, which should be

Consider the cavity QED parameters (*g*, *κ*, *κ*_{s}, *γ*), the final state of the system in unnormalized form is

The average fidelity of the scheme is

where cos *θ*_{A} = *α*, sin *θ*_{A} = *β*, cos *θ*_{A′} = *α*′, sin *θ*_{A′} = *β*′, cos *ϕ*_{B} = *γ*, sin *ϕ*_{B} = *ξ*, cos *ϕ*_{B′} = *γ*′, and sin *ϕ*_{B′} = *ξ*′. The fidelity of the scheme is unity in principle. The herald mechanism of the *g*, *κ*, *κ*_{s}, *γ*) and photon loss.

The efficiency of the scheme is defined as the probability that the hyperentangled photon pair are detected by the local single-photon detectors of Alice and Bob. In other words, the efficiency is the probability that none of the single-photon detectors of

which depends on cavity-QED parameters. The relation between the absolute amplitude of *r*_{−}(Δ), the cavity-QED parameters (*g*, *κ*, *κ*_{s}, *γ*), and the frequency detuning Δ is depicted in Figure 5, where we take *γ* = 0.01*κ*. As shown in Figure 5, we take the slices *g*/*κ* = 0.5, *g*/*κ* = 1, *g*/*κ* = 2.4, *κ*_{s}/*κ* = 0, *κ*_{s}/*κ* = 0.05, and *κ*_{s}/*κ* = 0.1 for examples. We can conclude that |*r*_{−}(Δ)| can get relevant high values not only around the resonant frequency Δ = 0 but also at some other frequency detuning such as Δ = ±*g*. The cavity side leakage and loss rate *κ*_{s}/*κ* decrease |*r*_{−}(Δ)| slightly.

**FIGURE 5**. The absolute amplitude |*r*_{−}(Δ)| of *r*_{−}(Δ) vs. the cavity QED parameters (*g*, *κ*, *κ*_{s}, *γ*) and the frequency detuning Δ. The slices shown are *g*/*κ* = 0.5, *g*/*κ* = 1, *g*/*κ* = 2.4, *κ*_{s}/*κ* = 0, *κ*_{s}/*κ* = 0.05, and *κ*_{s}/*κ* = 0.1. *γ* = 0.01*κ*.

When the system works under the resonance frequency (Δ = 0), the efficiency *η* is the function of the coupling strength *g*/*κ* and the cavity decay rate *κ*_{s}/*κ* under given *γ*. The relation between *η* and the cavity QED parameters (*g*, *κ*, *κ*_{s}, *γ*) under the resonant frequency Δ = 0 is shown in Figure 6. When the side leakage is negligible, the efficiency is 92.35% at *g* = 0.5*κ*, 98.021% at *g* = *κ*, and 99.65% at *g* = 2.4*κ*. The scheme has high efficiency without the strict requirement of the strong-coupling condition. When *κ*_{s} = 0.05*κ*, the efficiency is 62.26% at *g* = 0.5*κ*, 66.28% at *g* = *κ*, and 67.44% at *g* = 2.4*κ*. The scheme still works when the side leakage is taken into account. To obtain high efficiency, the side leakage and the cavity loss rate *κ*_{s}/*κ* should be controlled as small as possible. The side leakage *κ*_{s} can be reduced by engineering the fabrication and adjusting the material, structure and size of the cavity.

The hyperentangled photon pairs can be generated by combinations of the techniques used for creating entanglement in a single DOF [37, 38], such as with the assistance of an optical cavity [84, 85] or spontaneous four-wave mixing [86]. The bandwidth of the hyperentangled pules should be narrow than the linewidth of the cavity mode. The superposition state of an electron spin can be prepared assisted by nanosecond ESR pulses or picosecond optical pulses [53]. The fast single-qubit rotation operations on the electron spin can be achieved by ultrafast optical pulses or optically controlled geometric phases [54]. The dark counts of photon detectors may lead to false-positive responses that affect the efficiency slightly. Other factors such as the imperfect hyperentangled sources and the linear elements would affect the performance of the scheme, and can be improved by the manufacturing process.

In summary, assisted by single-sided QD-cavity systems, we presented two robust photon-spin hybrid CNOT gates with a herald mechanism, i.e., the *A* and *A*′ of Alice simultaneously control electron spins *B* and *B*′ of Bob, respectively. The scheme has some characteristics. First, we use hyperentangled photon pairs to build the quantum channel for nonlocal operations, which can effectively improve the channel capacity. Second, with the herald mechanism, the fidelities of the nonlocal CNOT gates can be raised to unity in principle. Third, teleporting two CNOT gates in parallel can save quantum resources and accelerate computing speed. Fourth, the scheme with the modular design has good flexibility. The advantages above make the scheme feasible with current technology, which may open promising possibilities for nonlocal quantum computation and quantum information networks. To construct a practical multi-node quantum network, a series of cascade cavities with coupled quantum memories or registers are required. Although our scheme could weaken the requirements for coupling strength and cavity leakage to some extent, it is still a technical challenge to connect multiple different cavities while keeping all cavities in the required coupling conditions. Therefore, we have great expectations for the optimization of microcavity parameters design and the improvement of the microfabrication process.

## Data availability statement

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

## Author contributions

All authors listed have made a substantial, direct, and intellectual contribution to the work and approved it for publication.

## Funding

The project was supported by Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications) (No. IPOC2022ZT07), P. R. China. This work was also supported by the National Natural Science Foundation of China (NSFC) under Grant Nos. 61701035 and 61671085.

## Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

## Publisher’s note

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Keywords: quantum network, quantum CNOT gate, quantum-dot spin, optical microcavity, hyperentanglement

Citation: Han Y-H, Cao C, Fan L and Zhang R (2022) Scheme for implementing nonlocal high-fidelity quantum controlled-not gates on quantum-dot-confined electron spins using optical microcavities and photonic hyperentanglement. *Front. Phys.* 10:1006255. doi: 10.3389/fphy.2022.1006255

Received: 29 July 2022; Accepted: 18 August 2022;

Published: 23 September 2022.

Edited by:

Tianyu Ye, Zhejiang Gongshang University, ChinaReviewed by:

Ma Hongyang, Qingdao University of Technology, ChinaChuan Wang, Beijing Normal University, China

Copyright © 2022 Han, Cao, Fan and Zhang . This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: Cong Cao, caocong@bupt.edu.cn