S. Bose, V. Vedral, P. L. Knight
We investigate the purification of entangled states by local actions using a variant of entanglement swapping. We show that there exists a measure of entanglement which is conserved in this type of purification procedure.
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Quantum communication is a secure way to transfer quantum information and to communicate with legitimate parties over distant places in a network. Although communication over a long distance has already been attained, technical problem arises due to unavoidable loss of information through the transmission channel. Quantum repeaters can extend the distance scale using entanglement swapping and purification scheme. Here we demonstrate the working of a quantum repeater by the above two processes. We use IBM's real quantum processor `ibmqx4' to create two pair of entangled qubits and design an equ…
We develop theoretical and numerical tools for the quantification of entanglement in systems with continuous degrees of freedom. Continuous variable entanglement swapping is introduced and based on this idea we develop methods of entanglement purification for continuous variable systems. The success of these entanglement purification methods is then assessed using these tools.
To Purify or Not to Purify: Entanglement Purification under Input Fidelity Asymmetry in Quantum Networks
研究探讨了在量子网络中因输入保真度不对称而进行纠缠净化的必要性，推导了保真度不对称容忍度公式，并提出DeltaPurify策略以优化净化决策。
We study the use of entanglement purification for quantum communication over long distances. For distances much longer than the coherence length of a corresponding noisy quantum channel, the fidelity of transmission is usually so low that standard purification methods are not applicable. It is however possible to divide the channel into shorter segments that are purified separately and then connected by the method of entanglement swapping. This method can be much more efficient than schemes based on quantum error correction, as it makes explicit use of two-way classical communication. An impor…
Chip-to-chip hyperentanglement distribution and entanglement purification using silicon integrated photonics
该研究首次在集成硅芯片间实现偏振-空间超纠缠分发，并通过消耗空间自由度完成纠缠纯化，弥补了片上量子中继器的关键环节。
In the framework of cavity QED, we propose a practical scheme to purify dynamically a bipartite entangled state using short chains of atoms coupled to high-finesse optical cavities. In contrast to conventional entanglement purification protocols, we avoid CNOT gates, thus reducing complicated pulse sequences and superfluous qubit operations. Our interaction scheme works in a deterministic way, and together with entanglement distribution and swapping, opens a route towards efficient quantum repeaters for long-distance quantum communication.
We study quantum entanglement distribution on networks with full-rank bi-partite mixed states linking qubits on nodes. In particular, we use entanglement swapping and purification to partially entangle widely separated nodes. The simplest method consists of performing entanglement swappings along the shortest chain of links connecting the two nodes. However, we show that this method may be improved upon by choosing a protocol with a specific ordering of swappings and purifications. A priori, the design that produces optimal improvement is not clear. However, we parametrize the choices and find…
Optimal Fidelity-Aware Entanglement Distribution in Linear Quantum Networks
该研究针对两链路线性量子网络的保真度最大化纠缠分发问题，证明纠缠交换和纯化分别等价于二分图与非二分图的最大权匹配，提出两种多项式算法并通过数值实验验证了PtS性能更优、StP省略纯化可获显著收益。
Toward Hop-Independent Fidelity in Quantum Data Centers: Resource Requirements for Entanglement Purification
研究通过黑盒模型分析量子数据中心中多跳分发导致的保真度损失，比较不同纯化协议的资源需求，发现多副本纯化显著提升可行性与效率。
Single-photon entanglement is a simple form of entanglement that exists between two spatial modes sharing a single photon. Despite its elementary form, it provides a resource as useful as polarization-entangled photons and it can be used for quantum teleportation and entanglement swapping operations. Here, we report the first experiment where single-photon entanglement is purified with a simple linear-optics based protocol. Besides its conceptual interest, this result might find applications in long distance quantum communication based on quantum repeaters.
Simulation of Quantum Repeater Networks under Decoherence and Purification Constraints
本研究提出一个模拟框架，用于在连续时间退极化噪声下分析链式量子中继器，通过实现纠缠生成、交换和纯化，揭示了存储退相干与纯化对性能的影响及成本随距离的扩展规律。
We study information-disturbance trade-off in generalized entanglement swapping protocols wherein starting from Bell pairs $\left(1,2\right)$ and $\left(3,4\right)$, one performs an arbitrary joint measurement on $\left(2,3\right)$, so that $\left(1,4\right)$ now becomes correlated. We obtain trade-off inequalities between information gain in correlations of $\left(1,4\right)$ and residual information in correlations of $\left(1,2\right)$ and $\left(3,4\right)$ respectively and argue that information contained in correlations (information) is conserved if each inequality is an equality. We sho…
Deterministic entanglement swapping of W states
本文提出确定性W态纠缠交换协议，通过量子电路设计和基于弱测量的纯化方法，在含噪条件下实现远程三方共享高保真W态。
In our previous paper [Phys. Rev. A 84, 042303 (2011)], we proposed an efficient scheme to purify dynamically a bipartite entangled state using short chains of atoms coupled to high-finesse optical cavities. In contrast to conventional entanglement purification protocols, we avoid controlled-NOT gates and thus reduce complicated pulse sequences and superfluous qubit operations. In this paper, we significantly improve the output fidelity of remotely entangled atoms by introducing one additional entanglement protocol in each of the repeater nodes and by optimizing the laser beams required to con…
It is known that entanglement swapping can be used to realize entanglement purifying. By this way, two particles belong to different non-maximally entangled pairs can be projected probabilisticly to a maximally entangled state or to a less entangled state. In this report, we show, when the less entangled state is obtained, if a unitary transformation is introduced locally, then a maximally entangled state can be obtained probabilisticly from this less entangled state. The total successful probability of our scheme is equal to the entanglement of a single pairpurification (if two original pairs…
We consider entanglement swapping, a key component of quantum network operations and entanglement distribution. Pure entangled states, which are the desired input to the swapping protocol, are typically mixed by environmental interactions causing a reduction in their degree of entanglement. Thus an understanding of entanglement swapping with partially mixed states is of importance. Here we present a general analytical solution for entanglement swapping of arbitrary two-qubit states. Our result provides a comprehensive method for analyzing entanglement swapping in quantum networks. First, we sh…
We present a detailed rate analysis for a hybrid quantum repeater assuming perfect memories and using optimal probabilistic entanglement generation and deterministic swapping routines. The hybrid quantum repeater protocol is based on atomic qubit-entanglement distribution through optical coherent-state communication. An exact, analytical formula for the rates of entanglement generation in quantum repeaters is derived, including a study on the impacts of entanglement purification and multiplexing strategies. More specifically, we consider scenarios with as little purification as possible and we…
We propose the use of hybrid entanglement in an entanglement swapping protocol, as means of distributing a Bell state with high fidelity to two parties, Alice and Bob. The hybrid entanglement used in this work is described as a discrete variable (Fock state) and a continuous variable (cat state superposition) entangled state. We model equal and unequal levels of photonic loss between the two propagating continuous variable modes, before detecting these states via a projective vacuum-one-photon measurement, and the other mode via balanced homodyne detection. We investigate homodyne measurement …
Entanglement Distribution in Quantum Repeater with Purification and Optimized Buffer Time
本文研究了具有优化缓冲时间、噪声存储器和不完美操作的量子中继器纠缠分发，发现操作不完美时单存储器纠缠率随存储器数量增加而降低，强调了现实条件下量子中继器设计需考虑有限且不完美的操作与资源。
Intelligence-Guided Adaptive Purification for DDoS-Resilient Quantum Networks: A CUDA-Q based Study
研究量子中继器网络在经典控制平面受攻击时自适应控制策略的权衡。开发CUDA-Q/SeQUeNCe联合仿真工作流，对比多种纯化策略，结果表明网络态势感知能通过牺牲原始吞吐量来提高量子网络中合格纠缠传递的保真度。
Capacity-Achieving Entanglement Purification Protocol for Pauli Dephasing Channel
本文提出了一种实现Pauli退相位通道容量的双向纠缠纯化协议，通过可扩展的电路实现渐进式保真度提升，有效抑制退相干误差。
Enhancing the teleportation fidelity of a quantum network using purification
本文分析并比较了不同拓扑结构量子网络在两种纠缠分发方案下的资源性，提出算法评估平均最大隐形传态保真度，证明基于纯化的方案能显著提升网络隐形传态能力。
We introduce measurement-based quantum repeaters, where small-scale measurement-based quantum processors are used to perform entanglement purification and entanglement swapping in a long-range quantum communication protocol. In the scheme, pre-prepared entangled states stored at intermediate repeater stations are coupled with incoming photons by simple Bell-measurements, without the need of performing additional quantum gates or measurements. We show how to construct the required resource states, and how to minimize their size. We analyze the performance of the scheme under noise and imperfect…
Distribution and Purification of Entanglement States in Quantum Networks
针对量子网络高保真纠缠态分发问题，提出基于动态规划和线性规划的最优EP分发算法，进一步给出高保真GHZ态分发的最优算法，通过NetSquid仿真验证了技术有效性。
Classical systems can be entangled. Entanglement is defined by coincidence correlations. Quantum entanglement experiments can be mimicked by a mechanical system with a single conserved variable and 77.8% conditional efficiency. Experiments are replicated for four particle entanglement swapping and GHZ entanglement.
As a direct consequence of the no-cloning theorem, the deterministic amplification as in classical communication is impossible for quantum states. This calls for more advanced techniques in a future global quantum network, e.g. for cloud quantum computing. A unique solution is the teleportation of an entangled state, i.e. entanglement swapping, representing the central resource to relay entanglement between distant nodes. Together with entanglement purification and a quantum memory it constitutes a so-called quantum repeater. Since the aforementioned building blocks have been individually demo…
Quantum switches are envisioned to be an integral component of future entanglement distribution networks. They can provide high quality entanglement distribution service to end-users by performing quantum operations such as entanglement swapping and entanglement purification. In this work, we characterize the capacity region of such a quantum switch under noisy channel transmissions and imperfect quantum operations. We express the capacity region as a function of the channel and network parameters (link and entanglement swap success probability), entanglement purification yield and application…
We consider the explicit construction of resource states for measurement-based quantum information processing. We concentrate on special-purpose resource states that are capable to perform a certain operation or task, where we consider unitary Clifford circuits as well as non-trace preserving completely positive maps, more specifically probabilistic operations including Clifford operations and Pauli measurements. We concentrate on $1 \to m$ and $m \to 1$ operations, i.e. operations that map one input qubit to $m$ output qubits or vice versa. Examples of such operations include encoding and dec…
Optimal Entanglement Routing in Quantum Repeater Chains: Beyond Fixed Operation Order and Purification Schedule
本研究针对量子中继链纠缠路由，提出统一优化框架，证明纯化调度（树形优于泵浦）是决定可行性的主导因素，而操作顺序为替代因素。
We present a "hybrid quantum repeater" protocol for the long-distance distribution of atomic entangled states beyond qubits. In our scheme, imperfect noisy entangled pairs of two qudits, i.e., two discrete-variable $d$-level systems, each of, in principle, arbitrary dimension $d$, are initially shared between the intermediate stations of the channel. This is achieved via local, sufficiently strong light-matter interactions, involving optical coherent states and their transmission after these interactions, and optical measurements on the transmitted field modes, especially (but not restricted t…
Where do entangled multiple-qubit systems store information? For information injected into a qubit, this question is nontrivial and interesting since the entanglement delocalizes the information. So far, a common picture is that of a qubit and its purification partner sharing the information quantum mechanically. Here, we introduce a new picture of a single qubit in the correlation space, referred to as quantum information capsule (QIC), confining the information perfectly. This picture is applicable for the entangled multiple-qubit system in an arbitrary state. Unlike the partner picture, in …
An operational probabilistic theory where all systems are classical, and all pure states of composite systems are entangled, is constructed. The theory is endowed with a rule for composing an arbitrary number of systems, and with a nontrivial set of transformations. Hence, we demonstrate that the presence of entanglement is independent of the existence of incompatible measurements. We then study a variety of phenomena occurring in the theory -- some of them contradicting both Classical and Quantum Theories -- including: cloning, entanglement swapping, dense coding, additivity of classical capa…
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