States Of Bipartite Quantum Systems Research Articles

Isomorphism of nonlocal sets of orthogonal product states in bipartite quantum systems

Isomorphism of nonlocal sets of orthogonal product states in bipartite quantum systems

Search for an efficient entanglement witness operator for bound entangled states in bipartite quantum systems

Entanglement detection problem is one of the important problem in quantum information theory. Gurvit (2014) showed that this problem is NP complete and thus this may be the possible reason that only one criterion is not sufficient to detect all entangled states. There are some powerful entanglement detection criterion such as partial transposition criterion, realignment criterion but it may not be possible to implement them successfully in the experiment. This situation can be avoided if the entanglement is detected through the construction of witness operator method. In this work, we take an analytical approach to construct a witness operator. To achieve this task, we first construct a linear map using partial transposition and realignment operation. Then we find some conditions on the parameters of the map for which the map represent a positive map. Further, we have constructed a Choi matrix corresponding to the map and have shown that it is not completely positive. We then construct an entanglement witness operator, which is based on the linear combination of the function of Choi matrix and the identity matrix and it can detect both NPTES and PPTES. Finally, we prove its efficiency by detecting several bipartite bound entangled states which were previously undetected by some well-known separability criteria. We also compared the detection power of our witness operator with three well-known powerful entanglement detection criteria, namely, dV criterion, CCNR criterion and the separability criteria based on correlation tensor (CT) proposed by Sarbicki et. al. and find that our witness operator detects more entangled states than these criterion.

Absolutely classical spin states

We introduce the concept of "absolutely classical" spin states, in analogy to absolutely separable states of bi-partite quantum systems. Absolutely classical states are states that remain classical under any unitary transformation applied to them. We investigate the maximum ball of absolutely classical states centered on the fully mixed state that can be inscribed into the set of classical states, and derive a lower bound for its radius as function of the total spin quantum number. The result is compared to the case of absolutely separable states.

Quantum discord for generalized bloch sphere states

In this study, for particular states of bipartite quantum system in 2 n × 2 m dimensional Hilbert space state, similar to m or n-qubit density matrices represented in Bloch sphere which we call them generalized Bloch sphere states (GBSS), we give an efficient optimization procedure so that analytic evaluation of quantum discord can be performed. Using this optimization procedure, we find an exact analytical formula for the optimum positive operator valued measure (POVM) that maximizes the measure of the classical correlation for these states. The presented optimization procedure is also used to show that for any concave entropy function the same POVMs are sufficient for quantum discord of mentioned states. Furthermore, we show that such optimization procedure can be used to calculate the geometric measure of quantum discord (GMQD) and then an explicit formula for GMQD is given. Finally, a complete geometric view is presented for quantum discord of GBSS.

Compact smallest eigenvalue expressions in Wishart–Laguerre ensembles with or without afixed trace

The degree of entanglement of random pure states in bipartite quantum systems can beestimated from the distribution of the extreme Schmidt eigenvalues. For a bipartition of sizeM ≥ N,these are distributed according to a Wishart–Laguerre ensemble (WL) of random matrices of sizeN × M, with a fixed-trace constraint. We first compute the distribution and moments ofthe smallest eigenvalue in the fixed-trace orthogonal WL ensemble for arbitraryM ≥ N. Our method is based on a Laplace inversion of the recursive results for the correspondingorthogonal WL ensemble given by Edelman. Explicit examples are given for fixedN andM, generalizing and simplifying earlier results. In the microscopic largeN limitwith M − N fixed, the orthogonal and unitary WL distributions exhibit universality after a suitablerescaling and are therefore independent of the constraint. We prove that very recent resultsgiven in terms of hypergeometric functions of matrix argument are equivalent to moreexplicit expressions in terms of a Pfaffian or determinant of Bessel functions. While thelatter were mostly known from the random matrix literature on the QCD Diracoperator spectrum, we also derive some new results in the orthogonal symmetryclass.

Bipartite quantum systems: on the realignment criterion and beyond

Inspired by the ‘computable cross norm’ or ‘realignment’ criterion, we propose a new point of view about the characterization of the states of bipartite quantum systems. We consider a Schmidt decomposition of a bipartite density operator. The corresponding Schmidt coefficients, or the associated symmetric polynomials, are regarded as quantities that can be used to characterize bipartite quantum states. In particular, starting from the realignment criterion, a family of necessary conditions for the separability of bipartite quantum states are derived. We conjecture that these conditions, which are weaker than the parent criterion, can be strengthened in such a way to obtain a new family of criteria that are independent of the original one. This conjecture is supported by numerical examples for the low dimensional cases. These ideas can be applied to the study of quantum channels, leading to a relation between the rate of contraction of a map and its ability to preserve entanglement.

Asymptotic Entanglement Manipulation of Bipartite Pure States

Entanglement of pure states of bipartite quantum systems has been shown to have a unique measure in terms of the von Neumann entropy of the reduced states of either of its subsystems. The measure is established under entanglement manipulation of an asymptotically large number of copies of the bipartite pure state. In this paper, two different asymptotic measures of entanglement for arbitrary sequences of bipartite pure states are established. These are shown to coincide only when the sequence is information stable, in terms of the quantum spectral information rates of its corresponding sequence of subsystem states. Additional bounds on the optimal rates of entanglement manipulation protocols in quantum information theory are also presented. These include bounds given by generalizations of the coherent information bounds, Rains' bound, and the relative entropy of entanglement.

Negative quantum conditional entropy and the entanglement measure of a kind of mixed state of bipartite quantum system

From negative quantum conditional entropy point of view this paper intestigates the entanglement measure of the prue state and a kind of mixed state of bipartite quantum system. Also this paper gives a definition of quantum conditional entropy of entanglement EA｜B(ρAB) and proves that it satisfies the four fundamental conditions of a entanglement measure for a kind of mixed state of 2×2 quantum system by this negative quantum conditional entropy Using conditional entropy of entanglement, this paper investigates the quantum entanglement between the two identical two-level atoms simultaneously interacting with vacuum cavity field as an application. This paper compares conditional entropy of entanglement and concurrence at the same condition, and the result shows that the curves of their evolvements are identical. These obtained results test and verifys that conditions of an entanglement measure may be taken as the entanglement measure of the prue state and a kind of mixed state of bipartite quantum system.

A simple spectral condition implying separability for states of bipartite quantum systems

For two qubits and for general bipartite quantum systems, we give a simple spectral condition in terms of the ordered eigenvalues of the density matrix which guarantees that the corresponding state is separable.

Characterizing entanglement with global and marginal entropic measures

We qualify the entanglement of arbitrary mixed states of bipartite quantum systems by comparing global and marginal mixednesses quantified by different entropic measures. For systems of two qubits we discriminate the class of maximally entangled states with fixed marginal mixednesses, and determine an analytical upper bound relating the entanglement of formation to the marginal linear entropies. This result partially generalizes to mixed states the quantification of entanglement with marginal mixednesses holding for pure states. We identify a class of entangled states that, for fixed marginals, are globally more mixed than product states when measured by the linear entropy. Such states cannot be discriminated by the majorization criterion.

Generalized entropies and quantum entanglement

We discuss the fundamental properties of general entropic forms based on arbitrary concave functions and their application to current problems of quantum information theory. It is first shown that the extended formalism allows to construct, for a two-qubit system, least biased density operators which possess minimum entanglement for any data based on Bell constraints, avoiding fake entanglement. We next discuss the generalized entropic criterion for separability of mixed states of bipartite quantum systems, and its relation with the disorder criterion.

Characterization of separable states and entanglement witnesses

We provide a canonical form of mixed states in bipartite quantum systems in terms of a convex combination of a separable state and a, so-called, edge state. We construct entanglement witnesses for all edge states. We present a canonical form of nondecomposable entanglement witnesses and the corresponding positive maps. We provide constructive methods for their optimization in a finite number of steps. We present a characterization of separable states using a special class of entanglement witnesses. Finally, we present a nontrivial necessary condition for entanglement witnesses and positive maps to be extremal.