Witness Operator Provides Better Estimate of the Lower Bound of Concurrence of Bipartite Bound Entangled States in $d_{1}\otimes d_{2}$ Dimensional System

TL;DR

This paper introduces a new family of witness operators that improve the estimation of the lower bound of concurrence for bipartite bound entangled states in arbitrary dimensions, surpassing previous methods.

Contribution

The authors construct a novel family of witness operators that better estimate the lower bound of concurrence for mixed entangled states in arbitrary bipartite systems.

Findings

Successfully detect many bound entangled states not identified by earlier methods.

Provide a more accurate lower bound estimate of concurrence for these states.

Demonstrate the effectiveness of the new witness operators in higher-dimensional systems.

Abstract

It is known that the witness operator is useful in the detection and quantification of entangled states. This motivated us for the construction of the family of witness operators that can detect many mixed entangled states. This family of witness operators is then used to estimate the lower bound of concurrence of the detected mixed entangled states. Our method of construction of witness operator is important in the sense that it will estimate a better lower bound of concurrence of the entangled states in arbitrary $d_{1}\otimes d_{2} (d_{1}\leq d_{2})$ dimensional system compared to the lower bound of the concurrence given in \cite{kchen}. We have shown the significance of our constructed witness operator by detecting many bound entangled states that are not detected by the earlier methods and then we use the expectation value of the witness operator to estimate the lower bound of the concurrence of those bound entangled states.