Physical realization of realignment criteria using structural physical approximation

TL;DR

This paper develops a physically realizable approximation of the realignment criterion for entanglement detection, enabling experimental implementation and detection of both NPT and PPT entangled states.

Contribution

It introduces a structural physical approximation of the realignment map, making it completely positive and experimentally accessible for entanglement detection.

Findings

The SPA-R map is completely positive and physically measurable.

The developed criterion detects both NPT and PPT entangled states.

Error analysis of the approximation is provided.

Abstract

Entanglement detection is an important problem in quantum information theory because quantum entanglement is a key resource in quantum information processing. Realignment criteria is a powerful tool for detection of entangled states in bipartite and multipartite quantum system. It is an important criteria for entanglement detection because it works well; not only for negative partial transpose entangled states (NPTES) but also for positive partial transpose entangled states (PPTES). Since the matrix corresponding to realignment map is indefinite so the experimental implementation of the map is an obscure task. In this work, firstly, we have approximated the realignment map to a positive map using the method of structural physical approximation (SPA) and then we have shown that the structural physical approximation of realignment map (SPA-R) 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 SPA-R map in the form of an inequality and have shown that the developed criterion not only detect NPTES but also PPTES. We have provided some examples to support the results obtained. Moreover, we have analysed the error that may occur because of approximating the realignment map.