Quantum Fisher information,quantum entanglement and correlation close to quantum critical phenomena

In this paper, we investigate the quantum Fisher information (QFI), quantum entanglement, quantum correlation and quantum phase transition (QPT) within the one-dimensional transverse Ising model by exploiting quantum renormalization-group method. The results show that quantum Fisher information, quantum entanglement, quantum correlation can evolve to two saturated values which exhibit QPT at the critical point after several iterations of the renormalization. Meanwhile, we find quantum entanglement or correlation can be detected perfectly by means of quantum Fisher information. Besides, it cannot capture any information about the system in the paramagnetic phase in view of quantum entanglement and correlation. Contrarily, it is evident the QFI is always nonzero even if the system is in the paramagnetic phase, i.e., the QFI can also be utilized as a highly favorable measure of quantum information in a broad of quantum spin systems. Furthermore, we disclose the nonanalytic and scaling behaviors of quantum Fisher information, which can be taken as a representation of quantum critical characterism.     

On Entangled Information and Quantum Capacity

The pure quantum entanglement is generalized to the case of mixed compound states to include the classical and quantum encodings as particular cases. The true quantum entanglements are characterized as transpose-CP but not CP maps. The entangled information is introduced as the relative entropy of the mutual and the input state and total information of the entangled states leads to two different types of entropy for a given quantum state: the von Neumann entropy, which is achieved as the supremum of the information over all c-entanglements, and the true quantum entropy, which is achieved at the standard entanglement. The q-capacity, defined as the supremum over all entanglements, doubles the c-capacity in the case of the simple algebra. The conditional q-entropy is positive, and q-information of a quantum channel is additive.     

Lower limits of spin detection efficiency for two-parameter two-qubit (TPTQ) states with non-ideal ferromagnetic detectors

We have investigated a TPTQ state as an input state of a non-ideal ferromagnetic detectors. Minimal spin polarization required to demonstrate spin entanglement according to entanglement witness and CHSH inequality with respect to (w.r.t.) their two free parameters have been found, and we have numerically shown that the entanglement witness is less stringent than the direct tests of Bell’s inequality in the form of CHSH in the entangled limits of its free parameters. In addition, the lower limits of spin detection efficiency fulfilling secure cryptographic key against eavesdropping have been derived. Finally, we have considered TPTQ state as an output of spin decoherence channel and the region of ballistic transmission time w.r.t. spin relaxation time and spin dephasing time has been found.     

量子纠缠和量子计算

量子纠缠是量子力学中的一种非经典现象。本文从介绍纠缠和纠缠态出发,着重讨论纠缠的本质和非定域性概念。文末还讨论了纠缠在量子计算中的作用：它是量子计算优于经典计算的重要原因之一。     

Abrupt decay of entanglement and quantum communication through noise channels

We investigate the dynamics of two qubits state through the Bloch channel. Starting from partially entangled states as input state, the output states are more robust compared with those obtained from initial maximally entangled states. Also the survivability of entanglement increased as the absolute equilibrium values of the channel increased or the ratio between the longitudinal and transverse relaxation times gets smaller. The ability of using the output states as quantum channels to perform quantum teleportation is investigated. The useful output states are used to send information between two users by using the original quantum teleportation protocol.     

Quantum Ergodic Theory and Communication Channels

The recently developed theory of the noncommutative dynamical entropy is applied to the theory of quantum communication channels. It is argued that the speed of information transmission is bounded by the dynamical entropy of the information carrier treated as a quantum dynamical system. The proof is given for two classes of communication channels. For the first one the input and output are classical devices which produce strings of bits, while for the second one the input and output messages are quantum states.     

适用网络的W态双服务器盲量子计算协议设计

结合实际的网络环境，为提高盲量子计算协议的执行效率和减少客户端占用量子服务器的时间，利用Bell态与W态的纠缠交换原理，提出了一种适用网络的双服务器盲量子协议方案。方案中客户端将计算任务分为两部分，并分别与Bob1和Bob2按照单服务器盲量子计算步骤执行完成。因为制备分别用于构造两台量子服务器中砖墙态的量子比特，只由一台量子计算机、执行一次制备过程就可以完成，与单服务器BQC相比并没有增加额外的量子服务器资源投入。方案可以实现客户端完全经典，协议具有无条件安全性。     

Quantum Phase Transition in Spin Systems Studied through Entanglement Estimators

Entanglement represents purely quantum effect involving two or more particles. Spin systems are good candidates for studying this effect and its relation with other collective phenomena ruled by quantum mechanics. While the presence of entangled states can be easily verified, the quantitative estimate of this property is still under investigation. One of the most useful tools in this framework is the concurrence whose definition, albeit limited to S = 1/2 systems, can be related to the correlators. We consider quantum spin systems defined along chains and square lattices, and described by Heisenberg-like Hamiltonians: our goal is to clarify the relation between entanglement and quantum phase transitions, as well as that between the concurrence the and the specific quantum state of the system.     

Compatible Information as a Natural Information Measure of a Quantum Channel

As a natural quantitative characteristic of mutual information contained in two compatible sets of quantum states considered as input and output, we introduce the Shannon amount of information corresponding to two independent general measurements of all possible quantum states of the input and output. We analyze the physical content of this information measure and its relation to other measures such as the Holevo information and coherent information. In an example of two two-level systems, the most important features of compatible information in the absence and presence of selection for measured states are revealed and discussed.     

Entanglement and multiple quantum coherence dynamics in spin clusters

With the purpose to reveal consistency between multiple quantum (MQ) coherences and entanglement, we investigate numerically the dynamics of these phenomena in one-dimensional linear chains and ring of nuclear spins 1/2 coupled by dipole–dipole interactions. As opposed to the calculation of the MQ coherence intensity based on the density matrix describing the spin system as a whole, we consider the “differentiated” intensity related only to the chosen spin pair based on the reduced density matrix. It is shown that the entanglement and the MQ coherence have similar dynamics only for nearest neighbors while we did not obtained any consistency for remote spins.     

Some Issues in Quantum Information Theory

Quantum information theory is a new interdisciplinary research field related to quantum mechanics, computer science, information theory, and applied mathematics. It provides completely new paradigms to do information processing tasks by employing the principles of quantum mechanics. In this review, we first survey some of the significant advances in quantum information theory in the last twenty years. We then focus mainly on two special subjects： discrimination of quantum objects and transformations between entanglements. More specifically, we first discuss discrimination of quantum states and quantum apparatus in both global and local settings. Secondly, we present systematical characterizations and equivalence relations of several interesting entanglement transformation phenomena, namely entanglement catalysis, multiple-copy entanglement transformation, and partial entanglement recovery.     

Quantum correlation via quantum coherence

Quantum correlation includes quantum entanglement and quantum discord. Both entanglement and discord have a common necessary condition—quantum coherence or quantum superposition. In this paper, we attempt to give an alternative understanding of how quantum correlation is related to quantum coherence. We divide the coherence of a quantum state into several classes and find the complete coincidence between geometric (symmetric and asymmetric) quantum discords and some particular classes of quantum coherence. We propose a revised measure for total coherence and find that this measure can lead to a symmetric version of geometric quantum correlation, which is analytic for two qubits. In particular, this measure can also arrive at a monogamy equality on the distribution of quantum coherence. Finally, we also quantify a remaining type of quantum coherence and find that for two qubits, it is directly connected with quantum nonlocality.     

基于序列输入的量子神经网络模型及算法

为提高神经网络的逼近能力,提出一种各维输入为离散序列的量子神经网络模型及算法.该模型为3层结构,隐层为量子神经元,输出层为普通神经元.量子神经元由量子旋转门和多位受控非门组成,利用多位受控非门中目标量子位的输出向输入端的反馈,实现对输入序列的整体记忆,利用受控非门输出中多位量子比特的纠缠获得量子神经元的输出.基于量子计算理论设计该模型的学习算法.该模型可从宽度和深度两方面获取输入序列的特征.仿真结果表明,当输入节点数和序列长度满足一定关系时,该模型明显优于普通神经网络.     

Asymptotic entanglement in quantum walks from delocalized initial states

We study the entanglement between the internal (spin) and external (position) degrees of freedom of the one-dimensional discrete time quantum walk starting from local and delocalized initial states whose time evolution is driven by Hadamard and Fourier coins. We obtain the dependence of the asymptotic entanglement with the initial dispersion of the state and establish a way to connect the asymptotic entanglement between local and delocalized states. We find out that the delocalization of the state increases the number of initial spin states which achieves maximal entanglement from two states (local) to a continuous set of spin states (delocalized) given by a simple relation between the angles of the initial spin state. We also carry out numerical simulations of the average entanglement along the time to confront with our analytical results.     

Multipartite entanglement in an XXZ spin chain with Dzyaloshinskii–Moriya interaction and quantum phase transition

We investigate the multipartite entanglement and trace distance of the one-dimensional anisotropic spin-1/2 XXZ spin chain with the Dzyaloshinskii–Moriya interaction and find that the Dzyaloshinskii–Moriya interaction can influence the entanglement distribution and increase the proportion of multipartite entanglement in the entanglement structure. Furthermore, we explore the quantum phase transition of the XXZ spin chain with Dzyaloshinskii–Moriya interaction by making use of the multipartite entanglement and trace distance along with the quantum renormalization group method. It is found that the first derivatives of renormalized multipartite entanglement and trace distance for the ground state have dramatic changes near the critical point, and the renormalized multipartite entanglement and trace distance obey the universal finite-size scaling laws in the vicinity of the quantum critical point.     

绝热量子搜索算法中的纠缠与能量分析

为了进一步研究量子纠缠与量子计算速度及能量的关系,通过计算von Neumann纠缠熵,分析了时间复杂度分别为O(N )和O(1)的绝热量子搜索算法的量子纠缠度随时间的变化关系,并对两者进行了比较.实验结果表明,量子纠缠对绝热量子计算的运行时间具有明显的影响,较大的纠缠可以导致更短的运行时间,反之亦然.同时对纠缠与能量的关系给出了一般性解释,即注入能量导致系统的纠缠增大,并因此缩短算法的运行时间.此外还分析了纠缠与量子系统初态的关系.实验表明系统初态形式不同,其纠缠度也不一样.初态为等幅叠加态的算法涉及的纠缠度明显大于初态为非等幅叠加态的算法.     

VENUS: A Geometrical Representation for Quantum State Visualization

Visualizations have played a crucial role in helping quantum computing users explore quantum states in various quantum computing applications. Among them, Bloch Sphere is the widely-used visualization for showing quantum states, which leverages angles to represent quantum amplitudes. However, it cannot support the visualization of quantum entanglement and superposition, the two essential properties of quantum computing. To address this issue, we propose VENUS, a novel visualization for quantum state representation. By explicitly correlating 2D geometric shapes based on the math foundation of quantum computing characteristics, VENUS effectively represents quantum amplitudes of both the single qubit and two qubits for quantum entanglement. Also, we use multiple coordinated semicircles to naturally encode probability distribution, making the quantum superposition intuitive to analyze. We conducted two well-designed case studies and an in-depth expert interview to evaluate the usefulness and effectiveness of VENUS. The result shows that VENUS can effectively facilitate the exploration of quantum states for the single qubit and two qubits.     

Quantum coherence behaviors of fermionic system in non-inertial frame

In this paper, we analyze the quantum coherence behaviors of a single qubit in the relativistic regime beyond the single-mode approximation. Firstly, we investigate the freezing condition of quantum coherence in fermionic system. We also study the quantum coherence tradeoff between particle and antiparticle sector. It is found that there exists quantum coherence transfer between particle and antiparticle sector, but the coherence lost in particle sector is not entirely compensated by the coherence generation of antiparticle sector. Besides, we emphatically discuss the cohering power and decohering power of Unruh channel with respect to the computational basis. It is shown that cohering power is vanishing and decohering power is dependent of the choice of Unruh mode and acceleration. Finally, we compare the behaviors of quantum coherence with geometric quantum discord and entanglement in relativistic setup. Our results show that this quantifiers in two region converge at infinite acceleration limit, which implies that this measures become independent of Unruh modes beyond the single-mode approximations. It is also demonstrated that the robustness of quantum coherence and geometric quantum discord are better than entanglement under the influence of acceleration, since entanglement undergoes sudden death.