Entanglement and statistical independence for mixed quantum states

We show that three conditions associated with “entanglement,”viz., non-locality, non-factorisability and statistical dependence, are equivalent for pure states, and that non-factorisability and statistical dependence are equivalent for mixed states. Discussion then reinforces the generally held view that the key condition for mixed states is nonseparability.     

Quantifying entanglement of two-qubit Werner states

In this article, we introduce a framework for entanglement quantification of photon pairs represented by two-qubit Werner states. The measurement scheme is based on the symmetric informationally complete POVM. To make the framework realistic, we impose the Poisson noise on the measured two-photon coincidences. For various settings, numerical simulations were performed to evaluate the efficiency of the framework.     

Entanglement evolution of three-qubit mixed states in multipartite cavity—reservoir systems

We analyze the multipartite entanglement evolution of three-qubit mixed states composed of a GHZ state and a W state.For a composite system consisting of three cavities interacting with independent reservoirs,it is shown that the entanglement evolution is restricted by a set of monogamy relations.Furthermore,as quantified by the negativity,the entanglement dynamical property of the mixed entangled state of cavity photons is investigated.It is found that the three cavity photons can exhibit the phenomenon of entanglement sudden death(ESD).However,compared with the evolution of a generalized three-qubit GHZ state which has the equal initial entanglement,the ESD time of mixed states is later than that of the pure state.Finally,we discuss the entanglement distribution in the multipartite system,and point out the intrinsic relation between the ESD of cavity photons and the entanglement sudden birth of reservoirs.     

Relative entropy of entanglement of two-qubit ’X’ states

Two closest single-qubit states could be diagonalised by the same unitary matrix,which helps to find the relative entropy of entanglement of a two-qubit ’X’ state.We formulate two binary equations for the relative entropy of entanglement and the corresponding closest separable state of a given two-qubit ’X’ state.This approach can be applied to get the relative entropy of entanglement of many widely-discussed two-qubit states,such as pure states,Werner states,and so on.     

Entanglement Capacity of Two-Qubit Unitary Operator with the Help of Auxiliary System

The＇entanglement capacity of general two-qubit unitary operators is studied when auxiliary systems are allowed, and the analytical results based on linear entropy when input states are disentangled are given. From the results the condition for perfect entangler, α1 = α2 = π/4, is obtained. Contrary to the case without auxiliary system, the parameter α3 may play active role to the entanglement capacity when auxiliary systems are allowed.     

Robustness of two-qubit and three-qubit states in correlated quantum channels

We investigate how the correlated actions of quantum channels affect the robustness of entangled states. We consider the Bell-like state and random two-qubit pure states in the correlated depolarizing, bit flip, bit-phase flip, and phase flip channels. It is found that the robustness of two-qubit pure states can be noticeably enhanced due to the correlations between consecutive actions of these noisy channels, and the Bell-like state is always the most robust one. We also consider the robustness of three-qubit pure states in correlated noisy channels. For the correlated bit flip and phase flip channels, the result shows that although the most robust and most fragile states are locally unitary equivalent, they exhibit different robustness in different correlated channels, and the effect of channel correlations on them is also significantly different. However, for the correlated depolarizing and bit-phase flip channels, the robustness of two special three-qubit pure states is exactly the same. Moreover, compared with the random three-qubit pure states, they are neither the most robust states nor the most fragile states.     

Entanglement dynamics of a moving multi-photon Jaynes-Cummings model in mixed states

Using the algebraic dynamical method,the entanglement dynamics of an atom-field bipartite system in a mixed state is investigated.The atomic center-of-mass motion and the field-mode structure are also included in this system.We find that the values of the detuning and the average photon number are larger,the amplitude of the entanglement is smaller,but its period does not increase accordingly.Moreover,with the increase of the field-mode structure parameter and the transition photon number,the amplitude of the entanglement varies slightly while the oscillation becomes more and more fast.Interestingly,a damping evolution of the entanglement appears when both the detuning and the atomic motion are considered simultaneously.     

Entanglement dynamics of a moving multi-photon Jaynesben Cummings model in mixed states

Using the algebraic dynamical method, the entanglement dynamics of an atom-field bipartite system in a mixed state is investigated. The atomic center-of-mass motion and the field-mode structure are also included in this system. We find that the values of the detuning and the average photon number are larger, the amplitude of the entanglement is smaller, but its period does not increase accordingly. Moreover, with the increase of the field-mode structure parameter and the transition photon number, the amplitude of the entanglement varies slightly while the oscillation becomes more and more fast. Interestingly, a damping evolution of the entanglement appears when both the detuning and the atomic motion are considered simultaneously.     

Properties on the distant distribution of entanglement for arbitrary two-qubit pure states via noisy quantum channels

This paper investigates the change of entanglement for transmitting an arbitrarily entangled two-qubit pure state via one of three typical kinds of noisy quantum channels: amplitude damping quantum channel, phase damping quantum channel and depolarizing quantum channel. It finds, in all these three cases, that the output distant entanglement (measured by concurrence) reduces proportionately with respect to its initial amount, and the decaying ratio is determined only by the noisy characteristics of quantum channels and independent of the form of initial input state.     

Relation between initial conditions and entanglement sudden death for two-qubit extended Werner-like states

In this paper, the dynamical behavior of entanglement of an uncoupled two-qubit system, which interacts with inde- pendent identical amplitude damping environments and is initially prepared in the extended Werner-like （EWL） states, is investigated. The results show that whether entanglement sudden death （ESD） of an EWL state will occur or not depends on initial purity and concurrence. The boundaries between ESD states and ESD-free states for two kinds of EWL states are found to be different. Furthermore, some regions are shown where ESD states can be transformed into ESD-free states by local unitary operations.     

Introducing the general condition for an operator in curved space to be unitary

We investigate the general condition for an operator to be unitary. This condition is introduced according to the definition of the position operator in curved space. In a particular case, we discuss the concept of translation operator in curved space followed by its relation with an anti-Hermitian generator. Also we introduce a universal formula for adjoint of an arbitrary linear operator. Our procedure in this paper is totally different from others, as we explore a general approach based only on the algebra of the operators. Our approach is only discussed for the translation operators in one-dimensional space and not for general operators.     

Entanglement of Formation for Quantum States

We investigate the entanglement of formation for a class of high-dimensional quantum mixed states. We present a kind of generalized concurrence for a class of high-dimensional quantum pure states such that the entanglement of formation is a monotonically increasing convex function of the generallzed concurrence, from the monotonicity and convexity the entanglement of formafion for a class of high-dimensional mixed states has been calculated analytically,     

N+2原子受简并双光子作用时的纠缠动力学

研究了N+2（其中N个原子与光场非共振作用,2个原子与光场共振作用）原子受简并双光子作用的纠缠动力学,得到2个共振原子的纠缠度的解析表达式。结果表明：在简并双光子作用下,纠缠度的时间演化出现有规则的崩塌回复现象,并且崩塌回复周期比单光子作用下时要短。此外,N+2原子与光场间的相对耦合系数对简并双光子情形下的纠缠度有更灵敏的影响。     

N+2原子受简并双光子作用时的纠缠动力学

研究了N+2（其中N个原子与光场非共振作用,2个原子与光场共振作用）原子受简并双光子作用的纠缠动力学,得到2个共振原子的纠缠度的解析表达式。结果表明：在简并双光子作用下,纠缠度的时间演化出现有规则的崩塌回复现象,并且崩塌回复周期比单光子作用下时要短。此外,N+2原子与光场间的相对耦合系数对简并双光子情形下的纠缠度有更灵敏的影响。     

利用V-型三能级原子与双模腔场 双光子大失谐相互作用制备W纠缠态

本文提出利用 型三能级原子与双模腔场的双光子大失谐相互作用制备W纠缠态,该方案要求三个三能级原子和一个双模腔场,第一个与腔场作用的原子最初处于激发态,第二个和第三个原子均处于基态,腔场最初处于真空态,合适地选择原子与腔场之间的相互作用时间即可获得三原子W纠缠态。并且此方案可以推广至多原子W纠缠态和多腔场W纠缠态的制备;通过计算共生纠缠度研究系统中态的纠缠演化以及热纠缠现象。     

利用V-型三能级原子与双模腔场双光子大失谐相互作用制备W纠缠态

本文提出利用V-型三能级原子与双模腔场的双光子大失谐相互作用制备W纠缠态,该方案要求三个三能级原子和一个双模腔场,第一个与腔场作用的原子最初处于激发态,第二个和第三个原子均处于基态,腔场最初处于真空态,合适地选择原子与腔场之间的相互作用时间即可获得三原子W纠缠态.并且此方案可以推广至多原子W纠缠态和多腔场W纠缠态的制备;通过计算共生纠缠度研究系统中态的纠缠演化以及热纠缠现象.     

Entanglement swapping of continuous variable using squeezed vacuum states

We present a realistic scheme for the entanglement swapping of continuous variable, in which a two-mode squeezed vacuum state serves as a quantum channel. The position sum and momentum difference of two local modes are measured. By taking the input entangled state also as a two-mode squeezed vacuum state, we investigate the average fidelity and the von Neumann entropy of the output state. The results show that the perfect teleportation can be achieved by increasing the squeezing of the quantum channel and that any nonzero squeezing in both the quantum channel and the input entangled state is sufficient to swap the entanglement.     

Avoiding the decay of entanglement for coupling two-qubit system interacting with a non-Markov environment

The entanglement evolution of the coupled qubits interacting with a non-Markov environment is investigated in terms of concurrence.The results show that the entanglement of the quantum systems depends not only on the initial state of the system but also on the coupling between the qubit and the environment.For the initial state （|00 ± |11） /2^1/2,the coupled qubits will always been in the maximum entangled state under an asymmetric coupling.For the initial state （|01 ± |10） /2^1/2,in contrast,the entangling degree of the coupled qubits is always equal to unity and does not depend on the evolving time under the symmetric coupling.We find that the stronger the interaction between the qubits is,the better the struggle against the entanglement sudden death is.