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

Abstract

Entanglement detection problem is one of the important problem in quantum information theory. Gurvit 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 detect more entangled states than these criterion.

Accepted in Annals of Physics. In this work, we propose a witness operator detects more entangled states than the other detection criteria, namely, dV criterion, CCNR criterion and separability criterion based on correlation tensor

References in corpus (5)

• Entanglement detection
• Bloch vectors for qudits
• Covariance matrices and the separability problem
• Witness Operator Provides Better Estimate of the Lower Bound of Concurrence of Bipartite Bound Entangled States in $d_1\otimes d_2$ Dimensional System
• Classification witness operator for the classification of different subclasses of three-qubit GHZ class

Cited by in corpus (2)

• Entanglement detection in arbitrary dimensional bipartite quantum systems through partial realigned moments
• Physical realization of realignment criteria using structural physical approximation