In this article we investigate the unitary dynamics of squashed entanglement and concurrence measures in Werner state and maximally entangled mixed states (MEMS) under two different Hamiltonians. The aim of the present study is two fold. The first part of the study deals with the dynamics under Heisenberg Hamiltonian and the second part deals under bi-linear bi-quadratic Hamiltonian which is the extension of first Hamiltonian. In both the parts we investigate the dynamical trade off and balancing points for squashed entanglement and concurrence. During the study, we also found the results of entanglement sudden death (ESD) with Heisenberg Hamiltonian in Werner state under concurrence measure. In second part, we investigate the special result for bi-linear bi-quadratic Hamiltonian; it does not disturb squashed entanglement and concurrence in both the states and exhibit the robust character for both of the states.
We propose a novel parameterized entanglement measure $α$-concurrence for bipartite systems. By employing positive partial transposition and realignment criteria, we derive analytical lower bounds for the $α$-concurrence. Moreover, we calculate explicitly the analytic expressions of the $α$-concurrence for isotropic states and Werner states.
In this work we propose the geometric mean of bipartite concurrences as a genuine multipartite entanglement measure. This measure achieves the maximum value for absolutely maximally entangled states and has desirable properties for quantifying potential quantum resources. The simplicity and symmetry in the definition facilitates its computation for various multipartite entangled states including the GHZ states and the $W$ states. With explicit examples we show that our measure results in distinct entanglement orderings from other measures, and can detect differences in certain types of genuine…
The problem on detecting the entanglement of a bipartite state is significant in quantum information theory. In this article, we apply the Ky Fan norm to the revised realignment matrix of a bipartite state. Specifially, we consider a family of separable criteria for bipartite states, and present when the density matrix corresponds to a state is real, the criteria is equivalent to the enhanced realignment criterion. Moreover, we present analytical lower bounds of concurrence and the convex-roof extended negativity for arbitrary dimensional systems.
我们讨论的纠缠措施称为I-并发和纠缠的性质。对于两体纯态，I-纠缠和纠缠只与边缘密度算符的纯度有关。二分混合态的I-共点（缠结）是联合密度算符的纯态系综分解的最小平均I-共点（缠结）。Terhal和Vollbrecht [Phys. Rev. Lett. 85，2625（2000）]给出了任意维各向同性态形成的纠缠的显式公式。我们使用他们的形式主义，以获得比较表达式的I-并发和纠缠的各向同性状态。
The problems of genuine multipartite entanglement detection and classification are challenging. We show that a multipartite quantum state is genuine multipartite entangled if the multipartite concurrence is larger than certain quantities given by the number and the dimension of the subsystems. This result also provides a classification of various genuine multipartite entanglement. Then, we present a lower bound of the multipartite concurrence in terms of bipartite concurrences. While various operational approaches are available for providing lower bounds of bipartite concurrences, our results …
Detection of entanglement in bipartite states is a fundamental task in quantum information. The first method to verify entanglement in mixed states was the partial-transpose criterion. Subsequently, numerous quantifiers for bipartite entanglement were introduced, among them concurrence and negativity. Surprisingly, these quantities are often treated as distinct or independent of each other. The aim of this contribution is to highlight the close relations between these concepts, to show the connections between seemingly independent results, and to present various estimates for the mixed-state c…
The squashed entanglement is a fundamental entanglement measure in quantum information theory, finding application as an upper bound on the distillable secret key or distillable entanglement of a quantum state or a quantum channel. This paper simplifies proofs that the squashed entanglement is an upper bound on distillable key for finite-dimensional quantum systems and solidifies such proofs for infinite-dimensional quantum systems. More specifically, this paper establishes that the logarithm of the dimension of the key system (call it $\log_{2}K$) in an $\varepsilon$-approximate private state…
Witness Operator Provides Better Estimate of the Lower Bound of Concurrence of Bipartite Bound Entangled States in $d_{1}\otimes d_{2}$ Dimensional System
One-qubit pure states, living on the surface of Bloch sphere, can be mapped onto the usual complex plane by using stereographic projection. In this paper, after reviewing the entanglement of two-qubit pure state, it is shown that the \emph{quaternionic} stereographic projection is related to concurrence measure. This is due to the fact that every two-qubit state, in ordinary complex field, corresponds to the one-qubit state in quaternionic skew field, called quaterbit. Like the one-qubit states in complex field, the stereographic projection maps every quaterbit onto a quaternion number whose c…
Entanglement concurrence has been widely used for featuring entanglement in quantum experiments. As an entanglement monotone it is related to specific quantum Tsallis entropy. Our goal in this paper is to propose a new parameterized bipartite entanglement monotone which is named as $q$-concurrence inspired by general Tsallis entropy. We derive an analytical lower bound for the $q$-concurrence of any bipartite quantum entanglement state by employing positive partial transposition criterion and realignment criterion, which shows an interesting relationship to the strong separability criteria. Th…
For bipartite quantum states we obtain lower bounds on two important entanglement measures, concurrence and negativity, studying the inequalities for the expectation value of a projector on some subspace of the Hilbert space. Several applications, including analysis of stability of entanglement under various perturbations of a state, are discussed.
Tight bounds on the concurrence of quantum superpositions
基于{ \it并发度}研究了量子态叠加的纠缠度。给定一个任意维的二分纯态，写为另外两个这样的状态的量子叠加，我们发现简单的不等式有关的状态，其组件的并发。我们推导出一个精确的表达式的并发时，组件状态是双正交的，并提供优雅的上限和下限在所有其他情况下。对于量子比特，我们的上限比先前在[Phys. Rev. Lett. 97，100502（2006）.]
The Schmidt coefficients capture all entanglement properties of a pure bipartite state and therefore determine its usefulness for quantum information processing. While the quantification of the corresponding properties in mixed states is important both from a theoretical and a practical point of view, it is considerably more difficult, and methods beyond estimates for the concurrence are elusive. In particular this holds for a quantitative assessment of the most valuable resource, the maximum possible Schmidt number of an arbitrary mixed state. We derive a framework for lower bounding the appr…
We analyse two possible definitions of the squashed entanglement in an infinite-dimensional bipartite system: direct translation of the finite-dimensional definition and its universal extension. It is shown that the both definitions produce the same lower semicontinuous entanglement measure possessing all basis properties of the squashed entanglement on the set of states having at least one finite marginal entropy. Is also shown that the second definition gives an adequate extension of this measure to the set of all states of infinite-dimensional bipartite system. A general condition relating …
