Separability criteria and bounds for entanglement measures

Abstract

Employing a recently proposed separability criterion we develop analytical lower bounds for the concurrence and for the entanglement of formation of bipartite quantum systems. The separability criterion is based on a nondecomposable positive map which operates on state spaces with even dimension N ≥ 4, and leads to a class of nondecomposable optimal entanglement witnesses. It is shown that the bounds derived here complement and improve the existing bounds obtained from the criterion of positive partial transposition and from the realignment criterion.

Entanglement of formation and concurrence for mixed states

“…Another lower bound of EOF for bipartite states on even dimensional Hilbert spaces N has been presented [29] from a new separability criterion [30]. On even dimensional spaces there exist antisymmetric unitary operations V T 5 2V.…”

“…If one takes the separability criterion (44) into account, the above bound can be improved [29]. Set f ppt (r) 5 ||r…”

“…In Ref. [29], another lower bound on EOF for bipartite states has been presented from a new separability criterion [30]. A lower bound on concurrence based on a local uncertainty relations (LURs) criterion is obtained in Ref.…”

Estimation of concurrence for multipartite mixed states

“…In [15,16] analytical lower bounds of EoF and concurrence for any dimensional mixed bipartite quantum states have been presented, which are further shown to be exact for some special classes of states and detect many bound entangled states. In [17] another lower bound of EoF for bipartite states has been presented from a new separability criterion.…”

Generalized monogamy relations of concurrence forN-qubit systems

“…For N -qubit systems ABC1...CN−2, the monogamy relations satisfied by the concurrence of N -qubit pure states under the partition AB and C1...CN−2, as well as under the partition ABC1 and C2...CN−2 are established, which give rise to a kind of restrictions on the entanglement distribution and trade off among the subsystems.PACS numbers: 03.67.Mn,03.65.UdQuantum entanglement [1][2][3][4][5][6] is an essential feature of quantum mechanics, which distinguishes the quantum from classical world. As one of the fundamental differences between quantum entanglement and classical correlations, a key property of entanglement is that a quantum system entangled with one of other systems limits its entanglement with the remaining others.…”