Simple Entanglement Measure for Multipartite Pure States

A simple entanglement measure for multipartite pure states is formulated based on the partial entropy of a series of reduced density matrices. Use of the proposed new measure to distinguish disentangled, partially entangled, and maximally entangled multipartite pure states is illustrated.     

Tractable Quantification of Entanglement for Multipartite Pure States

We present kth-order entanglement measure and global kth-order entanglement measure for multipartite pure states, and extend Bennett＇s measure of partial entropy for bipartite pure states to a multipaxtite case. These measures are computable and can effectively classify and quantify the entanglement of multipartite pure states.     

A New Multipartite Entanglement Measure for Arbitrary <Emphasis Type="Italic">n</Emphasis>-qudit Pure States

In this paper, we propose a multipartite entanglement measure for arbitrary pure states, which is presented based on reduced density matrices of multi-qudit pure states. We review some multipartite entanglement measures based on density matrices. This is helpful for us to introduce a new good entanglement measure, which is vanishing if and only if a state is separable, invariant under local unitary transformations and non-increasing under local operations assisted by classical communication. We apply our entanglement measure for some explicit examples. It demonstrates that our entanglement measure is practical and convenient for computation. It can also distinguish the relatively high entanglement and the maximal entanglement. In short, our entanglement measure is good at characterizing multipartite entanglement.     

Relative Entropy and Squashed Entanglement

We are interested in the properties and relations of entanglement measures. Especially, we focus on the squashed entanglement and relative entropy of entanglement, as well as their analogues and variants. Our first result is a monogamy-like inequality involving the relative entropy of entanglement and its one-way LOCC variant. The proof is accomplished by exploring the properties of relative entropy in the context of hypothesis testing via one-way LOCC operations, and by making use of an argument resembling that by Piani on the faithfulness of regularized relative entropy of entanglement. Following this, we obtain a commensurate and faithful lower bound for squashed entanglement, in the form of one-way LOCC relative entropy of entanglement. This gives a strengthening to the strong subadditivity of von Neumann entropy. Our result improves the trace-distance-type bound derived in Brandão et al. (Commun Math Phys, 306:805–830, 2011), where faithfulness of squashed entanglement was first proved. Applying Pinsker’s inequality, we are able to recover the trace-distance-type bound, even with slightly better constant factor. However, the main improvement is that our new lower bound can be much larger than the old one and it is almost a genuine entanglement measure. We evaluate exactly the relative entropy of entanglement under various restricted measurement classes, for maximally entangled states. Then, by proving asymptotic continuity, we extend the exact evaluation to their regularized versions for all pure states. Finally, we consider comparisons and separations between some important entanglement measures and obtain several new results on these, too.     

Entropic entanglement criteria for Fermion systems

Entanglement criteria for general (pure or mixed) states of systems consisting of two identical fermions are introduced. These criteria are based on appropriate inequalities involving the entropy of the global density matrix describing the total system, on the one hand, and the entropy of the one-particle reduced density matrix, on the other hand. A majorization-related relation between these two density matrices is obtained, leading to a family of entanglement criteria based on Rényi’s entropic measure. These criteria are applied to various illustrative examples of parametrized families of mixed states. The dependence of the entanglement detection efficiency on Rényi’s entropic parameter is investigated. The extension of these criteria to systems of N identical fermions is also considered.     

Death of entanglement and purity in a two qubits–field system induced by phase damping

We investigate the death of entanglement and the purity loss of a two qubits–field system in the dispersive regime with a reservoir. For an alternative entanglement measure, we calculate the negativity of the eigenvalues of a partially transposed density matrix and compare it with the mutual entropy. A new measure related to the mutual entropy, namely, the index of entropy, is proposed to measure the degree of entanglement, and this agrees well with the negativity. We found that the entanglement has a strong sensitivity to the phase damping. The asymptotic behavior of the field states, the two qubits, and the total system fall into a mixed state. We treat the phenomena of death of entanglement and purity as they arise from the effect of phase damping.     

Dynamical correlations of negativity and entropy for pure and mixed states in two coupled quartic oscillators

Various measures of entanglement have triggered considerable interest in the relationship between entanglement measures and other well-known quantities. As a demonstration, the dynamical correlation of negativity and entropy is studied in two coupled quartic oscillators for initial pure and mixed states that are respectively taken to be the products and mixed density matrices of coherent states and squeezed states on each oscillator. The correlation with energy is also considered. It is shown that for the initial pure states with a small magnitude, two negativities are positively correlated with the von Neumann entropy while they are anti-correlated with the energy of each oscillator in the weak coupling regime. For mixed states with a small magnitude the two negativities and the mutual entropy exhibit dominantly positive correlation, whereas those three quantities are dominantly anti-correlated with the sum of energies of two oscillators in the case of weak interactions. Such correlation behaviors in the mixed state with small magnitudes are most striking at the same step in maximal and minimal values and in oscillation. The differences in entropies and negativities between coherent states and squeezed states are discussed. These are useful for quantum entanglement and quantum information processing.     

Thermodynamical analogues in quantum information theory

The first step in quantum information theory is the identification of entanglement as a valuable resource. The next step is learning how to efficiently exploit this resource. We learn how to efficiently exploit entanglement by applying analogues of thermodynamical concepts. These concepts include reversibility, entropy, and the distinction between intensive and extensive quantities. We discuss some of these analogues and show how they lead to a measure of entanglement for pure states. We also ask whether these analogues are more than analogues, and note that, locally, entropy of entanglement is thermodynamical entropy.     

Sufficient and Necessary Conditions of Entanglement Transformations Between Mixed States

Based on a new measure of entanglement for finite-dimensional bi-particle pure states, we give sufficient and necessary conditions that a bi-particle mixed state ρ can be transformed into another mixed state σ by local operations and classical communication (LOCC). This result can be regarded as a generalization of Nielsen’s theorem (Nielsen, Phys. Rev. Lett. 83:436, 1999). However, we find that it is more difficult to determine the entanglement transformations between mixed states than to do between pure ones.     

Effect of Intrinsic Decoherence of Milburn＇s Model on Entanglement of Two-Qutrit States

We analyze the time evolution of entanglement of two-qutrit system within the framework of Milburn's model of intrinsic decoherence. The entanglement evolution relies not only on the parameters of system, but also on the concrete states either pure or mixed. The linear entropy used to measure the extent to which the intrinsic decoherence affects quantum states is evaluated.     

Quantifying entanglement in terms of an operational way

We establish entanglement monotones in terms of an operational approach,which is closely connected with the state conversion from pure states to the objective state by the local operations and classical communications.It is shown that any good entanglement quantifier defined on pure states can induce an entanglement monotone for all density matrices.Particularly,we show that our entanglement monotone is the maximal one among all those having the same form for pure states.In some special cases,our proposed entanglement monotones turn to be equivalent to the convex roof construction,which hence gain an operational meaning.Some examples are given to demonstrate different cases.     

Multipartite entanglement dynamics and decoherence

We study the dynamics of multipartite entanglement under decoherence induced by the environment consisting of a fermionic bath. Based on the algebraic measure of entanglement-negativity, we analyze the time evolution of entanglement of both pure states and mixed ones, and find that entanglement evolution depends on both bath temperature and the number of qubits of the system. A linear space S_LDF which is dynamically decoupled from the environment is identified in the sense of linear entropy to symbolize the environment effect.     

Aspects of Generic Entanglement

We study entanglement and other correlation properties of random states in high-dimensional bipartite systems. These correlations are quantified by parameters that are subject to the ``concentration of measure' phenomenon, meaning that on a large-probability set these parameters are close to their expectation. For the entropy of entanglement, this has the counterintuitive consequence that there exist large subspaces in which all pure states are close to maximally entangled. This, in turn, implies the existence of mixed states with entanglement of formation near that of a maximally entangled state, but with negligible quantum mutual information and, therefore, negligible distillable entanglement, secret key, and common randomness. It also implies a very strong locking effect for the entanglement of formation: its value can jump from maximal to near zero by tracing over a number of qubits negligible compared to the size of the total system. Furthermore, such properties are generic. Similar phenomena are observed for random multiparty states, leading us to speculate on the possibility that the theory of entanglement is much simplified when restricted to asymptotically generic states. Further consequences of our results include a complete derandomization of the protocol for universal superdense coding of quantum states.     

Entanglement of electronic subbands and coherent superposition of spin states in a Rashba nanoloop

The present work is concerned with an analysis of the entanglement between the electronic coherent superpositions of spin states and subbands in a quasi-one-dimensional Rashba nanoloop acted upon by a strong perpendicular magnetic field. We explicitly include the confining potential and the Rashba spin-orbit coupling into the Hamiltonian and then proceed to calculate the von Neumann entropy, a measure of entanglement, as a function of time. An analysis of the von Neumann entropy demonstrates that, as expected, the dynamics of entanglement strongly depends upon the initial state and electronic subband excitations. When the initial state is a pure one formed by a subband excitation and the z-component of spin states, the entanglement exhibits periodic oscillations with local minima (dips). On the other hand, when the initial state is formed by the subband states and a coherent superposition of spin states, the entanglement still periodically oscillates, exhibiting stronger correlations, along with elimination of the dips. Moreover, in the long run, the entanglement for the latter case undergoes the phenomenon of collapse-revivals. This behaviour is absent for the first case of the initial states. We also show that the degree of entanglement strongly depends upon the electronic subband excitations in both cases.     

Generalized measures of quantum correlations for mixed states

The exponential speedup achieved in certain quantum algorithms based on mixed states with negligible entanglement has renewed the interest on alternative measures of quantum correlations. Here we discuss a general measure of quantum correlations for composite systems based on generalized entropic functions, defined as the minimum information loss due to a local measurement. For pure states, the present measure becomes an entanglement entropy, i.e., it reduces to the generalized entropy of the reduced state. However, for mixed states it can be nonzero in separable states, vanishing just for states diagonal in a general product basis, like the quantum discord. Quadratic measures of quantum correlations can be derived as particular cases of the present formalism. The minimum information loss due to a joint local measurement is also considered. The evaluation of these measures in a simple yet relevant case is also discussed.     

Degree of Entanglement and Violation of Bell Inequality by Two-Spin-1/2 States

Bell inequality is violated by the quantum mechanical predictions made from an entangled state of the composite system. In this paper we examine this inequality and entanglement measures in the construction of the coherent states for two-qubit pure and mixed states. we find a link to some entanglement measures through some new parameters (amplitudes of coherent states). Conditions for maximal entanglement and separability are then established for both pure and mixed states. Finally, we analyze and compare the violation of Bell inequality for a class of mixed states with the degree of
entanglement by applying the formalism of Horodecki et al.     

Universal measure of entanglement

A general framework is developed for separating classical and quantum correlations in a multipartite system. Entanglement is defined as the difference in the correlation information encoded by the state of a system and a suitably defined separable state with the same marginals. A generalization of the Schmidt decomposition is developed to implement the separation of correlations for any pure, multipartite state. The measure based on this decomposition is a generalization of the entanglement of formation to multipartite systems, provides an upper bound for the relative entropy of entanglement, and is directly computable on pure states. The example of pure three-qubit states is analyzed in detail, and a classification based on minimal, four-term decompositions is developed.     

Bounds on bipartitely shared entanglement reduced from superposed tripartite quantum states

For a tripartite pure state superposed by two individual states, the bipartitely shared entanglement can always be achieved by local measurements of the third party. Consider the different aims of the third party, i.e. maximizing or minimizing the bipartitely shared entanglement, we find bounds on both the possible bipartitely shared entanglement of the superposition state in terms of the corresponding entanglement of the two states being superposed. In particular, by choosing the concurrence as bipartite entanglement measure, we obtain calculable bounds for tripartite (2 ⊗ 2 ⊗ n)-dimensional cases.     

费米环境中两个三能级原子系统的纠缠演化

利用负性纠缠度(negativity)研究了两个三能级原子系统在费米环境中的纠缠演化问题-结果表明,两个三能级原子系统的纠缠演化不仅依赖于系统和环境的相互作用强度,而且还依赖于系统所处的具体量子态-通过例子发现,系统和环境相互作用强度越大,纠缠衰减越快;对于纯态,仅当时间趋于无穷时纠缠才被完全破坏;对于混态,则在有限的时间内纠缠即被彻底破坏-通过一般的分析找到了一类免退相干的量子子空间-在这些子空间中,量子态不受环境的影响,故其纠缠不变-研究有助于理解费米环境造成的退相干对玻色系统纠缠的影响- 关键词： 费米环境 纠缠演化 两个三能级原子