Design and Implementation of Quantum Repeaters:Insights on Quantum Entanglement Purification

Quantum communication is a groundbreaking technology that is driving the future of information transmission and communication technologies to a new paradigm.It relies on quantum entanglement to facilitate the transmission of quantum states between parties.Quantum repeaters are crucial for facilitating long-distance quantum communication.These quantum devices act as intermediaries between adjacent communication channel segments within a fragmented quantum network,allowing for entanglement swapping between the channel segments.This entanglement swapping process establishes entanglement links between the endpoints of adjacent segments,gradually creating a continuous entanglement connection over the entire length of the transmission channel.The established quantum link can be utilized for secure and efficient quantum communication between distant sender and receiver nodes.This study focuses on quantum entanglement purification,a protocol aimed at maintaining high fidelity entangled states above the operational threshold of the communication channel.This study investigates the optimal stage for executing the purification protocol and applies optimization schemes to evaluate various purification protocols.We use IBM Qiskit for circuit implementation and simulation.The results offer valuable insights into future approaches to implementing practical quantum repeaters and shed light on existing and anticipated challenges.

Efficient entanglement purification in quantum repeaters

We present an efficient entanglement purification protocol （EPP） with controlled-not （CNOT） gates and linear optics. With the CNOT gates, our EPP can reach a higher fidelity than the conventional one. Moreover, it does not require the fidelity of the initial mixed state to satisfy 1 2. If the initial state is not entangled, it still can be purified. With the linear optics, this protocol can get pure maximally entangled pairs with some probabilities. Meanwhile, it can be used to purify the entanglement between the atomic ensembles in distant locations. This protocol may be useful in long-distance quantum communication.

Entanglement Purification Through Cavity Input-Output Process

We propose a scheme to purify entanglement of two atoms from not-too-impure entangled states by checking the parity of the two atoms through the cavity input-output process. As the parity check is made by measurement on single-photon polarization, which would not affect the entanglement of the two atoms, our scheme has the successful probability double of that in a previous well-known scheme with linear optical elements [Nature （London） 410 （2001） 1067], and is insensitive to the photon loss and the detection inefficieney. Experimental feasibility of our scheme with current technology is discussed.

Multi-copy entanglement purification with practical spontaneous parametric down conversion sources

Entanglement purification is to distill the high quality entanglement from the low quality entanglement with local operations and classical communications. It is one of the key technologies in long-distance quantum communication. We discuss an entanglement purification protocol（EPP） with spontaneous parametric down conversion（SPDC） sources, in contrast to previous EPP with multi-copy mixed states, which requires ideal entanglement sources. We show that the SPDC source is not an obstacle for purification, but can benefit the fidelity of the purified mixed state. This EPP works for linear optics and is feasible in current experiment technology.

Fast multi-copy entanglement purification with linear optics

We describe an entanglement purification protocol for a polarization Bell state. Different from the previous protocols,it does not require the controlled-not gate, and only uses linear optical elements to complete the task. This protocol requires multi-copy degraded mixed states, which can make this protocol obtain a high fidelity in one purification step. It can also be extended to purify the multi-photon Greenberger–Horne–Zeilinger（GHZ） state. This protocol may be useful in future long-distance communication.

Self-error-rejecting multipartite entanglement purification for electron systems assisted by quantum-dot spins in optical microcavities

We present a self-error-rejecting multipartite entanglement purification protocol(MEPP)for N-electron-spin entangled states,resorting to the single-side cavity-spin-coupling system.Our MEPP has a high efficiency containing two steps.One is to obtain high-fidelity N-electron-spin entangled systems with error-heralded parity-check devices(PCDs)in the same parity-mode outcome of three electron-spin pairs,as well as M-electron-spin entangled subsystems(2≤M<N)in the different parity-mode outcomes of those.The other is to regain the N-electron-spin entangled systems from Melectron-spin entangled states utilizing entanglement link.Moreover,the quantum circuits of PCDs make our MEPP works faithfully,due to the practical photon-scattering deviations from the finite side leakage of the microcavity,and the limited coupling between a quantum dot and a cavity mode,converted into a failed detection in a heralded way.

Heralded entanglement purification protocol using high-fidelity parity-check gate based on nitrogen-vacancy center in optical cavity

The decoherence of entangled states caused by the noisy channel is a salient problem for reducing the fidelity of quantum communication.Here we present a heralded two-photon entanglement purification protocol(EPP)using heralded high-fidelity parity-check gate(HH-PCG),which can increase the entanglement of nonlocal two-photon polarization mixed state.The HH-PCG is constructed by the input-output process of nitrogen-vacancy(NV)center in diamond embedded in a single-sided optical cavity,where the errors caused by the imperfect interaction between the NV center-cavity system and the photon can be heralded by the photon detector.As the unwanted components can be filtrated due to the heralded function,the fidelity of the EPP scheme can be enhanced considerably,which will increase the fidelity of quantum communication processing.

Advances in quantum entanglement purification

Since its discovery,the quantum entanglement becomes a promising resource in quantum communication and computation.However,the entanglement is fragile due to the presence of noise in quantum channels.Entanglement purification is a powerful tool to distill high quality entangled states from the low quality entangled states.In this review,we present an overview of entanglement purification,including the basic entanglement purification theory,the entanglement purification protocols(EPPs)with linear optics,EPPs with cross-Kerr nonlinearities,hyperentanglement EPPs,deterministic EPPs,and measurement-based EPPs.We also review experimental progress of EPPs in linear optics.Finally,we give the discussion on potential outlook for the future development of EPPs.This review may pave the way for practical implementations in future long-distance quantum communication and quantum network.

Experimental one-step deterministic polarization entanglement purification

Entanglement purification is to distill high-quality entangled states from low-quality entangled states.It is a key step in quantum repeaters,determines the efficiency and communication rates of quantum communication protocols,and is hence of central importance in long-distance communications and quantum networks.In this work,we report the first experimental demonstration of deterministic entanglement purification using polarization and spatial mode hyperentanglement.After purification,the fidelity of polarization entanglement arises from 0.268±0.002 to 0.989±0.001.Assisted with robust spatial mode entanglement,the total purification efficiency can be estimated as 10^(9) times that of the entanglement purification protocols using two copies of entangled states when one uses the spontaneous parametric down-conversion sources.Our work may have the potential to be implemented as a part of full repeater protocols.

Measurement-based entanglement purification for entangled coherent states

The entangled coherent states(ECSs)have been widely used to realize quantum information processing tasks.However,the ECSs may suffer from photon loss and decoherence due to the inherent noise in quantum channel,which may degrade the fidelity of ECSs.To overcome these obstacles,we present a measurement-based entanglement purification protocol(MBEPP)for ECSs to distill some highquality ECSs from a large number of low-quality copies.We first show the principle of this MBEPP without considering the photon loss.After that,we prove that this MBEPP is feasible to correct the error resulted from the photon loss.Additionally,this MBEPP only requires to operate the Bell state measurement without performing local two-qubit gates on the noisy pairs and the purified high-quality ECSs can be preserved for other applications.This MBEPP may have application potential in the implementation of long-distance quantum communication.

Entanglement purification for memory nodes in a quantum network

The entanglement between quantum memory nodes is a prerequisite in a quantum network, and the diamond nitrogen-vacancy(NV) center is a promising candidate serving as a quantum memory node. Here, we investigate the possibility of achieving an entanglement purification protocol(EPP) for entangled NV centers in distant diamonds. To construct the EPP, we design a nondestructive parity-check detector(PCD) utilizing an auxiliary polarization-entangled photon pair, which makes our EPP less time consuming and insensitive to the phase fluctuation of the optical path length. The satisfied fidelity of an NV center pair after purification and efficiency of obtaining a purified NV center pair with our EPP can be obtained with current experimental techniques in the realistic condition. This EPP is useful for a quantum network in which NV centers are used as quantum memory nodes.