Physical realization of realignment criteria using the structural physical approximation
Abstract
Entanglement detection is an important problem in quantum information theory because quantum entanglement is a key resource in quantum information processing. Realignment criterion is a powerful tool for the detection of entangled states in bipartite and multipartite quantum systems. It works well not only for negativepartialtranspose entangled states (NPTESs) but also for positivepartialtranspose entangled states (PPTESs). Since the matrix corresponding to the realignment map is indefinite, the experimental implementation of the map is an obscure task. In this work, first, we approximate the realignment map to a positive map using the method of structural physical approximation, and then we show that the structural physical approximation of the realignment map (SPAR) is completely positive. Positivity of the constructed map is characterized using moments which can be physically measured. Next, we develop a separability criterion based on our SPAR map in the form of an inequality and show that the developed criterion not only detect NPTESs but also PPTESs. Further, we show that for a special class of states called Schmidtsymmetric states, the SPAR separability criteria reduce to the original form of the realignment criteria. We provide some examples to support the results obtained. Moreover, we analyze the error that may occur because of approximating the realignment map.
 Publication:

Physical Review A
 Pub Date:
 July 2023
 DOI:
 10.1103/PhysRevA.108.012422
 arXiv:
 arXiv:2301.09884
 Bibcode:
 2023PhRvA.108a2422A
 Keywords:

 Quantum Physics
 EPrint:
 13 pages, 7 figures, 1 table, Appendix, Accepted in Physical Review A