Concentration Effect of Quantum and Classical Correlations during Quantum Brachistochrone Evolution

We explore the role of quantum brachistochrone evolution to quantum and classical correlations in three-qubit systems, and show that the time-averaged correlations of three-qubit systems exhibit an obvious concentration effect, which means both the standard deviations of time-averaged quantum and classical correlations decrease with the separation angle. Furthermore, we find that the concentration effect on genuine tripartite entanglement is the most significant during the quantum brachistochrone evolution of three-qubit systems.     

Aspects of Entanglement in Quantum Many-Body Systems

Knowledge of the entanglement properties of the wave functions commonly used to describe quantum many-particle systems can enhance our understanding of their correlation structure and provide new insights into quantum phase transitions that are observed experimentally or predicted theoretically. To illustrate this theme, we first examine the bipartite entanglement contained in the wave functions generated by microscopic many-body theory for the transverse Ising model, a system of Pauli spins on a lattice that exhibits an order-disorder magnetic quantum phase transition under variation of the coupling parameter. Results for the single-site entanglement and measures of two-site bipartite entanglement are obtained for optimal wave functions of Jastrow-Hartree type. Second, we address the nature of bipartite and tripartite entanglement of spins in the ground state of the noninteracting Fermi gas, through analysis of its two- and three-fermion reduced density matrices. The presence of genuine tripartite entanglement is established and characterized by implementation of suitable entanglement witnesses and stabilizer operators. We close with a broader discussion of the relationships between the entanglement properties of strongly interacting systems of identical quantum particles and the dynamical and statistical correlations entering their wave functions.     

BCS Effect on Quantum Correlation and Tripartite Quantum Entanglement in Spinless Gapless Tomonaga-Luttinger Liquid and Cuprate Superconducting Nanowire

It has been known that quantum information offers powerful instruments to investigate the properties of many-body systems. In this framework, we touched two particular aspect of this activity, namely the quantum entanglement and discord to compare the properties of gapless Tomonaga-Luttinger Liquid (TLL) model and the effect of BCS coupling in spinless fermions of TLL as a cuprate superconducting nanowire. Using two-fermion space-spin density matrix, we investigate quantum correlation of these cases via bipartite and tripartite entanglement, as well as quantum discord. The relations of concurrence (as a measure of quantum entanglement), the lower bound of the generalized robustness of tripartite entanglement and quantum discord in terms of the relative distance between fermions and the coupling parameter were accordingly obtained. The relationship between the compressibility as a physical property of system and quantum correlations has also been studied.

     

Continuous-Variable Quantum Teleportation of Entangled Coherent States

We propose a quantum teleportation scheme for tripartite entangled coherent state （ECS） with continuous variable. Our scheme is feasible and economical in the sense that we need only linear optical devices such as beam splitters, phase shifters and photon detectors and employ three bipartite maximally ECSs as quantum channels. We also generalize the tripartite scheme into multipartite ease and calculate the minimum average fidelity for the schemes in tripartite and multipartite cases.     

极性分子摆动态的三体量子关联

极性分子具有较长的相干时间和较强的偶极-偶极相互作用,因此它被视为量子信息处理的有效量子载体.基于分子摆动态作为量子比特,研究了处于热平衡状态下三极性分子线性链系统的三体量子关联特性,分析了三体负性熵纠缠度、测量诱导扰动和三体量子失协随与电场强度、分子电偶极矩、分子转动常数、偶极-偶极相互作用和温度等参数有关的三个无量纲变量之间的变化关系.研究表明:在其他参数给定的情况下,随电场强度的增加,三体量子关联均变小;随偶极-偶极相互作用强度的增大,三体量子关联先增加到峰值再逐渐变小;温度越高,负性熵纠缠度和三体量子失协越小,但测量诱导扰动随温度的改变在电场强度和偶极-偶极相互作用影响下呈现不同的变化趋势.此外,通过调节电场强度、偶极-偶极相互作用和温度,可改变与操控极性分子摆动态的三体量子关联.     

Dynamics of Super Quantum Correlations and Quantum Correlations for a System of Three Qubits

The dynamics of quantum discord for two qubits independently interacting with dephasing reservoirs have been studied recently.The authors [Phys.Rev.A 88(2013) 034304] found that for some Bell-diagonal states(BDS)which interact with their environments the calculation of quantum discord could experience a sudden transition in its dynamics,this phenomenon is known as the sudden change.Here in the present paper,we analyze the dynamics of normal quantum discord and super quantum discord for tripartite Bell-diagonal states independently interacting with dephasing reservoirs.Then,we find that basis change does not necessary mean sudden change of quantum correlations.     

Multipartite Quantum Coherence and Distribution under the Unruh Effect

Quantum coherence of the tripartite W state and Greenberger–Horne–Zeilinger (GHZ) state under the Unruh effect are explored based on the model of a two‐level detector qubit coupled to a massless scalar field. The results reveal that Unruh thermal noise really destroys tripartite quantum resources. It is worth mentioning that the quantum coherence of the GHZ state reaches zero in the infinite acceleration limit, but that of the W‐state always remains nonzero. Coherence of the GHZ state displays a sudden death as the coupling parameter grows, while coherence freezing can be witnessed for the W state. It can be concluded that the W state is more robust than the GHZ state against Unruh radiation. Moreover, the related investigation can be expanded to N‐qubit quantum systems and the corresponding analytical solution is obtained. It indicates that the larger number W‐type entangled qubit can be as a better quantum resource for quantum information tasks under the Unruh effect.     

New Tripartite Nonlinear Entangled State Representation in Quantum Mechanics

Based on the technique of integral within an ordered product of nonlinear bosonic operators, we construct a new kind of tripartite nonlinear entangled state |α,γ〉_λ in 3-mode Fock space, which can make up a complete set. We also simply discuss its properties and application.     

Characterizing Quantum Correlations in Arbitrary-Dimensional Bipartite Systems Using Hurwitz's Theory

Quantum correlations play vital roles in the quantum features in quantum information processing tasks. Among the measures of quantum correlations, quantum discord （QD） and entanglement of formation （EOF） axe two significant ones. Recent research has shown that there exists a relation between QD and EOF, which makes QD more significant in quantum information theory. However, until now, there exists no general method of chaxaeterizing quantum discord in high-dimensional quantum systems. In this paper, we have proposed a general method for calculating quantum discord in axbitraxy-dimensionM bipaxtite quantum systems in terms of Hurwitz＇s theory. Applications including the Werner state, the spin-1 XXZ model thermal equilibrium state, the Horodecki state, and the separable-bound-free entanglement state are investigated. We present the method of obtaining the EOF of axbitraxy-dimensional bipaxtite quantum states via purification, and the relations.hip between QD and EOF.     

Additivity Relations of Quantum Correlations for Three-qubit Entangled State in Atom-cavity System

Taking advantage of quantum discord and negativity respectively, four additivity relations of quantum correlations are studied in the atom-cavity system, for three identical two-level atoms resonantly interact with a single-mode high-Q cavity simultaneously. Through numerical analysis, we find that in this model of atom-cavity system, four additivity relations of negativity are always satisfied well, no matter tripartite are in the pure states or the mixed states, while the results of quantum discord are not always satisfied. What’s more, if and only if the mixed three-atom states evolve into the pure states again, four additivity inequality relations of quantum discord and negativity become equalities simultaneously.     

Dynamics and protection of tripartite quantum correlations in a thermal bath

We study the dynamics and protection of tripartite quantum correlations in terms of genuinely tripartite concurrence, lower bound of concurrence and tripartite geometric quantum discord in a three-qubit system interacting with independent thermal bath. By comparing the dynamics of entanglement with that of quantum discord for initial GHZ state and W state, we find that W state is more robust than GHZ state, and quantum discord performs better than entanglement against the decoherence induced by the thermal bath. When the bath temperature is low, for the initial GHZ state, combining weak measurement and measurement reversal is necessary for a successful protection of quantum correlations. But for the initial W state, the protection depends solely upon the measurement reversal. In addition, the protection cannot usually be realized irrespective of the initial states as the bath temperature increases.     

周期轨道的量子化与量子能谱中的长程关联

用二维可积系统的半经典量子化方案和二维无关联振子系统的量子能级与周期轨道之间的对应关系,讨论了一组量子能级之间具有长程关联的内在机制,在二维无关联振子系统中,发现了具有相同拓扑M(M1,M2)的周期轨道相对应的量子能级之间存在着长程关联,并以二维4次无关联振子系统为例做了具体说明.     

Intrinsic Relations of Bipartite Quantum Resources in Tripartite Systems

Quantum resources play crucial roles for displaying superiority in many quantum communication and computation tasks. To reveal the intrinsic relations hidden in these quantum resources, many efforts have been made in recent years. In this work, the correlations of the tripartite W‐type states based on bipartite quantum resources are investigated. The inter‐relations among the degree of coherence, concurrence, Bell nonlocality, and purity are presented. Considering Bell nonlocal and Bell local (satisfied the Clauser–Horne–Shimony–Holt inequality) states for the two‐qubit subsystems derived from the tripartite W‐type states, exact lower and upper boundaries of the degree of coherence versus concurrence are obtained. Interestingly, exact relation among the degree of coherence, concurrence, and purity is obtained. Moreover, coherence is also closely related to entanglement in two specific scenarios: the tripartite W‐type state under decoherence and a practical system for a renormalized spin‐1/2 Heisenberg model.     

Tripartite Arbitrary Two-Qutrit Quantum State Sharing

A tripartite scheme for securely sharing an arbitrary unknown two-qutrit state is proposed, where two generalized Greenberger-Horne-Zeilinger （GHZ） states serve as the quantum channel linking the three legitimate parties. The quantum information （i.e., the arbitrary unknown two-qutrit state） from the sender can be split in such a way that it can be reconstructed deterministically by any agent via a proper unitary operation provided that both agents collaborates together. Moreover, the generalization of the tripartite scheme to more-party case is also outlined.     

Simulation of Topological Field Theories¶by Quantum Computers

Quantum computers will work by evolving a high tensor power of a small (e.g. two) dimensional Hilbert space by local gates, which can be implemented by applying a local Hamiltonian H for a time t. In contrast to this quantum engineering, the most abstract reaches of theoretical physics has spawned “topological models” having a finite dimensional internal state space with no natural tensor product structure and in which the evolution of the state is discrete, H≡ 0. These are called topological quantum field theories (TQFTs). These exotic physical systems are proved to be efficiently simulated on a quantum computer. The conclusion is two-fold: 1. TQFTs cannot be used to define a model of computation stronger than the usual quantum model “BQP”. 2. TQFTs provide a radically different way of looking at quantum computation. The rich mathematical structure of TQFTs might suggest a new quantum algorithm. Received: 4 May 2001 / Accepted: 16 January 2002     

Hamiltonian Formulation of Statistical Ensembles and Mixed States of Quantum and Hybrid Systems

Representation of quantum states by statistical ensembles on the quantum phase space in the Hamiltonian form of quantum mechanics is analyzed. Various mathematical properties and some physical interpretations of the equivalence classes of ensembles representing a mixed quantum state in the Hamiltonian formulation are examined. In particular, non-uniqueness of the quantum phase space probability density associated with the quantum mixed state, Liouville dynamics of the probability densities and the possibility to represent the reduced states of bipartite systems by marginal distributions are discussed in detail. These considerations are used to study ensembles of hybrid quantum-classical systems. In particular, nonlinear evolution of a single hybrid system in a pure state and unequal evolutions of initially equivalent ensembles are discussed in the context of coupled hybrid systems.     

Entanglement witnesses of four-qubit tripartite separable quantum states

A quantum entangled state is easily disturbed by noise and degenerates into a separable state. Compared to the entanglement with bipartite quantum systems, less progress has been made for the entanglement with multipartite quantum systems. For tripartite separability of a four-qubit system, we propose two entanglement witnesses, each of which corresponds to a necessary condition of tripartite separability. For the four-qubit GHZ state mixed with a W state and white noise, we prove that the necessary conditions of tripartite separability are also sufficient at W states side.     

Quantum ergodicity and energy flow in molecules

We review a theory for coupled many-nonlinear oscillator systems that describes quantum ergodicity and energy flow in molecules. The theory exploits the isomorphism between quantum energy flow in Fock space, that is, vibrational state space, and single-particle quantum transport in disordered solid-state systems. The quantum ergodicity transition in molecules is thereby analogous to the Anderson transition in disordered solids. The theory reviewed here, local random matrix theory (LRMT), describes the nature of the quantum ergodicity transition, statistical properties of vibrational eigenstates, and quantum energy flow through the vibrational states of molecules. Predictions of LRMT have been observed in computational studies of coupled nonlinear oscillator systems, which are summarized here. We also review applications of LRMT to molecular spectroscopy and chemical reaction rate theory, including adoption of LRMT in theories that predict rates of conformational change of molecules taking place at energies corresponding to those below and above the quantum ergodicity transition. A number of specific examples are reviewed, including the application of LRMT to predict (1) dilution factors of IR spectra of organic molecules, (2) rates of conformational change in chemical and photochemical reactions, (3) conformational dynamics of biological molecules in molecular beams, (4) rates of hydrogen bond breaking and rearrangement in clusters of biological molecules and water, and (5) excited state proton transfer reactions in proteins.