Entanglement complexity of lattice ribbons

We consider a discrete ribbon model for double-stranded polymers where the ribbon is constrained to lie in a three-dimensional lattice. The ribbon can be open or closed, and closed ribbons can be orientable or nonorientable. We prove some results about the asymptotic behavior of the numbers of ribbons withn plaquettes, and a theorem about the frequency of occurrence of certain patterns in these ribbons. We use this to derive results about the frequency of knots in closed ribbons, the linking of the boundary curves of orientable closed ribbons, and the twist and writhe of ribbons. We show that the centerline and boundary of a closed ribbon are both almost surely knotted in the infinite-n limit. For an orientable ribbon, the expectation of the absolute value of the linking number of the two boundary curves increases at least as fast as n, and similar results hold for the twist and writhe.     

Efficient three-step entanglement concentration for an arbitrary four-photon cluster state

We propose an entanglement concentration protocol to concentrate an arbitrary partially-entangled four-photon cluster state.As a pioneering three-step entanglement concentration scheme,our protocol only needs a single-photon resource to assist the concentration in each step,which makes this protocol more economical.With the help of the linear optical elements and weak cross-Kerr nonlinearity,one can obtain a maximally-entangled cluster state via local operations and classical communication.Moreover,the protocol can be iterated to obtain a higher success probability and is feasible under current experimental conditions.     

Investigations into quantum correlation of coupled qubits in a squeezed vacuum reservoir

In this paper,we investigate the quantum correlation of coupled qubits which are initially in maximally entangled mixed states in a squeezed vacuum reservoir.We compare and analyze the effects of squeezed parameters on quantum discord and quantum concurrence.The results show that in a squeezed vacuum reservoir,the quantum discord and quantum concurrence perform with completely opposite behaviors with the change of squeezed parameters.Quantum discord survives longer with the increase of squeezed amplitude parameter,but entanglement death is faster on the contrary.The results also indicate that the classical correlation of the system is smaller than quantum discord in a vacuum reservoir,while it is bigger than quantum discord in a squeezed vacuum reservoir.The quantum discord and classical correlation are more robust than quantum concurrence in the two reservoir environments,which indicates that the entanglement actually is easily affected by decoherence and quantum discord has a stronger ability to avoid decoherence in a squeezed vacuum reservoir.     

与Glauber-Lachs态相互作用的双原子间的纠缠演化

利用全量子理论,对伴随多光子跃迁时与Glauber-Lachs态相互作用的两个原子间的纠缠特性进行了研究,主要讨论了相干平均光子数、热平均光子数和跃迁光子数对系统中原子间的纠缠特性的影响.结果表明:系统中原子间的纠缠度是相干平均光子数的非单调函数;随着热平均光子数和跃迁光子数的增加,系统中原子间的纠缠度有减小的趋势,伴随双光子跃迁时系统中原子间的纠缠度随时间的演化呈现周期性.     

Effects of Bond Alternation on the Ground-State Phase Diagram of One-Dimensional XXZ Model

The ground-state properties and quantum phase transitions (QPTs) of the one-dimensional bond-alternative XXZ model are investigated by the infinite time-evolving block decimation (iTEBD) method.The bond-alternative effects on its ground-state phase diagram are discussed in detail.Once the bond alternation is taken into account,the antiferromagnetic phase (Δ 1) will be destroyed at a given critical point and change into a disordered phase without nonlocal string order.The QPT is shown to be second-order,and the whole phase diagram is provided.For the ferromagnetic phase region (Δ-1),the critical point r c always equals 1 (independent of Δ),and the QPT for this case is shown to be first-order.The dimerized Heisenberg model is also discussed,and two disordered phases can be distinguished by with or without nonlocal string orders.Both the bipartite entanglement and the fidelity per site,as two kinds of model-independent measures,are capable of describing all the QPTs in such a quantum model.     

基于四波混频过程和线性分束器产生四组份纠缠

多组份纠缠是量子信息处理的重要资源,它的产生通常涉及到许多复杂的线性和非线性过程.本文从理论上提出了一种利用两个独立的四波混频过程和线性分束器产生真正的四组份纠缠的方案,其中,线性分束器的作用是将两个独立的四波混频过程联系起来.首先应用部分转置正定判据研究了强度增益对四组份纠缠的影响,结果表明,在整个增益区域内都存在真正的四组份纠缠,并且随着强度增益的增加,纠缠也在增强.然后研究了线性分束器的透射率对四组份纠缠的影响,发现只要线性分束器的透射率不为0或1,该系统也可以产生真正的四组份纠缠.最后,通过研究该系统可能存在的三组份纠缠和两组份纠缠来揭示该系统的纠缠结构.本文理论结果为实验上利用原子系综四波混频过程产生真正的四组份纠缠提供了可靠的方案.     

Order-Stability in Complex Biological,Social, and AI-Systems from Quantum Information Theory

This paper is our attempt, on the basis of physical theory, to bring more clarification on the question “What is life?” formulated in the well-known book of Schrödinger in 1944. According to Schrödinger, the main distinguishing feature of a biosystem’s functioning is the ability to preserve its order structure or, in mathematical terms, to prevent increasing of entropy. However, Schrödinger’s analysis shows that the classical theory is not able to adequately describe the order-stability in a biosystem. Schrödinger also appealed to the ambiguous notion of negative entropy. We apply quantum theory. As is well-known, behaviour of the quantum von Neumann entropy crucially differs from behaviour of classical entropy. We consider a complex biosystem S composed of many subsystems, say proteins, cells, or neural networks in the brain, that is, S=(Si). We study the following problem: whether the compound system S can maintain “global order” in the situation of an increase of local disorder and if S can preserve the low entropy while other Si increase their entropies (may be essentially). We show that the entropy of a system as a whole can be constant, while the entropies of its parts rising. For classical systems, this is impossible, because the entropy of S cannot be less than the entropy of its subsystem Si. And if a subsystems’s entropy increases, then a system’s entropy should also increase, by at least the same amount. However, within the quantum information theory, the answer is positive. The significant role is played by the entanglement of a subsystems’ states. In the absence of entanglement, the increasing of local disorder implies an increasing disorder in the compound system S (as in the classical regime). In this note, we proceed within a quantum-like approach to mathematical modeling of information processing by biosystems—respecting the quantum laws need not be based on genuine quantum physical processes in biosystems. Recently, such modeling found numerous applications in molecular biology, genetics, evolution theory, cognition, psychology and decision making. The quantum-like model of order stability can be applied not only in biology, but also in social science and artificial intelligence.     

Switching and Swapping of Quantum Information: Entropy and Entanglement Level

Information switching and swapping seem to be fundamental elements of quantum communication protocols. Another crucial issue is the presence of entanglement and its level in inspected quantum systems. In this article, a formal definition of the operation of the swapping local quantum information and its existence proof, together with some elementary properties analysed through the prism of the concept of the entropy, are presented. As an example of the local information swapping usage, we demonstrate a certain realisation of the quantum switch. Entanglement levels, during the work of the switch, are calculated with the Negativity measure and a separability criterion based on the von Neumann entropy, spectral decomposition and Schmidt decomposition. Results of numerical experiments, during which the entanglement levels are estimated for systems under consideration with and without distortions, are presented. The noise is generated by the Dzyaloshinskii-Moriya interaction and the intrinsic decoherence is modelled by the Milburn equation. This work contains a switch realisation in a circuit form—built out of elementary quantum gates, and a scheme of the circuit which estimates levels of entanglement during the switch’s operating.     

远距离三原子量子纠缠特性与其应用

三原子分别被束缚在用光纤环形连接单侧泄漏微光学腔场中,在微腔中输入激光驱动场和施加局域激光场,利用输入-输出技术及绝热近似理论,推导出一维Ising链模型的有效哈密顿量,该哈密顿量表明该系统会诱导出三原子中的任意两原子纠缠及三原子纠缠,用伴随数(concurrence)度量两原子纠缠,用内禀纠缠度量三原子纠缠,通过数值计算,给出两原子和三原子纠缠随时间演化曲线,通过适当调控激光驱动场和局域激光场,在远距离三原子中任意两原子实现未知量子态的隐形传送。     

Effect of entanglement embedded in environment on quantum non-Markovianity based on collision model

By means of collision models(CMs) where the environment is simulated by a collection of ancillas consisting of two entangled qubits, we investigate the effects of entanglement in the environment on the non-Markovianity of an open quantum system. Two CMs are considered in this study, in the first one the open quantum system S directly collides with the environment,while in the second one the system interacts with two intermediate qubits which, in turn, are coupled to the environment. We show that it is possible to enhance the non-Markovianity by environment entanglement in both models. In particular, in the second model, we show that the initial state of the auxiliary qubits can also affect the non-Markovianity of the system and there exists the optimal combination of the initial environmental state and the initial state of auxiliary qubits. In this case, the non-Markovianity can be greatly enhanced.