Separability of Pure States of the Quantum Network of Three Nodes

This article discusses the complete separability and partial separability of the pure states of the quantum network of three nodes by means of the criterion of entanglement in terms of the covariance correlation tensor in quantum network theory.     

Separability of Mixed States of the Quantum Network of Three Nodes

This article discusses the complete separability and partial separability of the mixed states of quantum network of three nodes by means of the crJterlon of entanglement in terms of the covarJance correlation tensor in quantum network theory.     

Complete and Partial Separability Conditions of Mixed State for a Quantum Network of Any Nodes

By using the block division method in matrix calculus, this article successfully calculate the expectation values of the generating operators and the correlation tensors for quantum network of any nodes. Thence, by means of the criterion of entanglement in terms of the covariance correlation tensor in quantum network theory, this article discusses the complete and partial separability conditions of the mixed quantum state for a quantum network of any nodes and judge the separability of a quantum state in the general case of any nodes for two examples.     

General Solution for the Complete Separability of a Pure Quantum State with Real Coefficients for a Quantum Network of Any Nodes

By means of the criterion of entanglement in terms of the covariance correlation tensor in quantum network theory, this article discusses the general solution for the complete separability of the pure quantum state with real coefficients for a quantum network of any nodes.     

General Solution for the Complete Separability of a Pure Quantum State with Real Coefficients for a Quantum Network of Any Nodes

By means of the criterion of entanglement in terms of the covariance correlation tensor in quantum network theory, this article discusses the generalsolution for the complete separability of the pure quantum state with real coefficients for a quantum network of any nodes.     

Separability of Pure States and Mixed States of the Quantum Network of Two Nodes

This article discusses the separability of the pure states and mixed states of the quantum network of twonodes by means of the criterion of no entanglement in terms of the covariance correlation tensor in quantum networktheory, i.e. for a composite system consisting of two nodes. The covariance correlation tensor Mjk(1, 2) is equal to zerofor all possible j and k.     

Complete and Partial Separability Conditions of Mixed State for a Quantum Network of Any Nodes

By using the block division method in matrix calculus, this article successfully calculate the expectationvalues of the generating operators and the correlation tensors for quantum network of any nodes. Thence, by meansof the criterion of entanglement in terms of the covariance correlation tensor in quantum network theory, this articlediscusses the complete and partial separability conditions of the mixed quantum state for a quantum network of anynodes and judge the separability of a quantum state in the generalcase of any nodes for two examples.     

Separability of Pure and Mixed States of the Quantum Network of Four Nodes

This article discusses the separability of the pure and mixed states of the quantum network of four nodesby means of the criterion of entanglement in terms of the covariance correlation tensor in quantum network theory.     

Separability of Mixed States of the Quantum Network of Three Nodes

This article discusses the complete separability and partial separability of the mixed states of quantumnetwork of three nodes by means of the criterion of entanglement in terms of the covariance correlation tensor in quantumnetwork theory.     

Separability of Pure States of the Quantum Network of Three Nodes

This article discusses the complete separability and partial separability of the pure states of the quantumnetwork of three nodes by means of the criterion of entanglement in terms of the covariance correlation tensor in quantumnetwork theory.     

Quantum information density and network

We present a quantum information network in which quantum information density is used for performing quantum computing or teleportation. The photons are entangled in quantum channels and play a role of flying ebit to transmit interaction among the nodes. A particular quantum Gaussian channel is constructed; it permits photon-encoded information to transmit quantum signals with certain quantum parallelism. The corresponding quantum dynamical mutual information is discussed, and the controlling nodes connectivity by driving the network is studied. With regard to different driving functions, the connectivity distribution of the network is complicated. They obey positive or negative power law, and also influence the assortativity coefficient or the dynamical property of the network.      

Quantum Key Distribution in Large Scale Quantum Network Assisted by Classical Routing Information

Recently, small-scale Quantum Key Distribution (QKD) networks have been demonstrated and continuously operated in field environment. However, nodes of these QKD networks are less than 10 nodes. When the scale and structure of these networks becomes large and complex, such networks will subject to problem of intractable routing selection and limited transmission distance. We present a novel quantum network model and the corresponding protocol to solve these problems. The proposed quantum network model integrates classical communication network with quantum key distribution layer. Nodes in this quantum network model are divided into communication nodes for classical communication and quantum nodes for quantum key distribution. We use atomic ensembles to create entangled photons inside quantum nodes. Quantum repeaters are used to establish entanglement between remote quantum nodes so the maximum distribution distance of entangled photons can be extended. The main idea is to establish an appropriate key distribution path in the quantum key distribution layer based on the routing information obtained by the upper classical communication network. After the entanglement has been established between remote quantum nodes, these nodes will use the Ekert91 or BBM92 protocol to generate secret keys shared between each other. Then, these keys can be used to ensure the security of communication in the classical communication network.     

Quantum Stochastic Walk models for quantum state discrimination

Quantum Stochastic Walks (QSW) allow for a generalization of both quantum and classical random walks by describing the dynamic evolution of an open quantum system on a network, with nodes corresponding to quantum states of a fixed basis. We consider the problem of quantum state discrimination on such a system, and we solve it by optimizing the network topology weights. Finally, we test it on different quantum network topologies and compare it with optimal theoretical bounds.     

On the Lattice Structure of Probability Spaces in Quantum Mechanics

Let $\mathcal{C}$ be the set of all possible quantum states. We study the convex subsets of $\mathcal{C}$ with attention focused on the lattice theoretical structure of these convex subsets and, as a result, find a framework capable of unifying several aspects of quantum mechanics, including entanglement and Jaynes’ Max-Ent principle. We also encounter links with entanglement witnesses, which leads to a new separability criteria expressed in lattice language. We also provide an extension of a separability criteria based on convex polytopes to the infinite dimensional case and show that it reveals interesting facets concerning the geometrical structure of the convex subsets. It is seen that the above mentioned framework is also capable of generalization to any statistical theory via the so-called convex operational models’ approach. In particular, we show how to extend the geometrical structure underlying entanglement to any statistical model, an extension which may be useful for studying correlations in different generalizations of quantum mechanics.     

统计可分隔性与超光速量子通讯不可能

分析了量子力学中的空间关联与通讯的关系与差别,提出了统计可分隔性概念, 由此证明了超光速量子通讯不可能.We analyse the relation and the difference between the quantum correlation of two points in space and the communication between them. The statistical separability of two points in the space is defined and proven. From this statistical separability, we prove that the superluminal quantum communication betwcen different points is impossible. To emphasis the compatibility between the quantum theory and the relativity, we write the von Neumann equation of density operator evolution in the multi time form.     

Quantum multicast communication over the butterfly network

We propose a scheme where one can exploit auxiliary resources to achieve quantum multicast communication with network coding over the butterfly network.In this paper,we propose the quantum 2-pair multicast communication scheme,and extend it to k-pair multicast communication over the extended butterfly network.Firstly,an EPR pair is shared between each adjacent node on the butterfly network,and make use of local operation and classical communication to generate entangled relationship between non-adjacent nodes.Secondly,each sender adds auxiliary particles according to the multicast number k,in which the CNOT operations are applied to form the multi-particle entangled state.Finally,combined with network coding and free classical communication,quantum multicast communication based on quantum measurements is completed over the extended butterfly network.Not only the bottleneck problem is solved,but also quantum multicast communication can be completed in our scheme.At the same time,regardless of multicast number k,the maximum capacity of classical channel is 2 bits,and quantum channel is used only once.     

Quantum computing by optical control of electron spins

We review the progress and main challenges in implementing large-scale quantum computing by optical control of electron spins in quantum dots (QDs). Relevant systems include self-assembled QDs of III–V or II–VI compound semiconductors (such as InGaAs and CdSe), monolayer fluctuation QDs in compound semiconductor quantum wells, and impurity centres in solids, such as P-donors in silicon and nitrogen-vacancy centres in diamond. The decoherence of the electron spin qubits is discussed and various schemes for countering the decoherence problem are reviewed. We put forward designs of local nodes consisting of a few qubits which can be individually addressed and controlled. Remotely separated local nodes are connected by photonic structures (microcavities and waveguides) to form a large-scale distributed quantum system or a quantum network. The operation of the quantum network consists of optical control of a single electron spin, coupling of two spins in a local nodes, optically controlled quantum interfacing between stationary spin qubits in QDs and flying photon qubits in waveguides, rapid initialization of spin qubits and qubit-specific single-shot non-demolition quantum measurement. The rapid qubit initialization may be realized by selectively enhancing certain entropy dumping channels via phonon or photon baths. The single-shot quantum measurement may be in situ implemented through the integrated photonic network. The relevance of quantum non-demolition measurement to large-scale quantum computation is discussed. To illustrate the feasibility and demand, the resources are estimated for the benchmark problem of factorizing 15 with Shor's algorithm.     

Federated Quantum Machine Learning

Distributed training across several quantum computers could significantly improve the training time and if we could share the learned model, not the data, it could potentially improve the data privacy as the training would happen where the data is located. One of the potential schemes to achieve this property is the federated learning (FL), which consists of several clients or local nodes learning on their own data and a central node to aggregate the models collected from those local nodes. However, to the best of our knowledge, no work has been done in quantum machine learning (QML) in federation setting yet. In this work, we present the federated training on hybrid quantum-classical machine learning models although our framework could be generalized to pure quantum machine learning model. Specifically, we consider the quantum neural network (QNN) coupled with classical pre-trained convolutional model. Our distributed federated learning scheme demonstrated almost the same level of trained model accuracies and yet significantly faster distributed training. It demonstrates a promising future research direction for scaling and privacy aspects.     

Criteria for Separability of Multipartite Quantum System

We first present the Hamel base of the density operator space for multipartite quantum system, and thus establish a representation of density matrix. Moreover, according to the structure of the density matrix for multipartite quantum system, we present two necessary criteria for separability of multipartite quantum system of arbitrary dimensions.     

Quantum State Transfer Between Any Pair of Qubits in a Quantum Network via Optical Fibers

We propose scheme for transferring quantum state between any pair of nodes in a quantum network. Each node consists of an atom and a cavity, with the atom acting as the quantum bit. Any two adjacent nodes are connected by an optical fiber. During the operation neither the atomic system nor the fibers are excited, which is important in view of decoherence. Under certain conditions, the probability that the cavities are excited is negligible. The method has an inherent robustness against the fluctuation perturbations in the classical control parameters and the randomness in the atomic position. The scheme can be generalized to implement quantum phase gate between any two remote qubits.