Witness Operator Provides Better Estimate of the Lower Bound of Concurrence of Bipartite Bound Entangled States in $d_1\otimes d_2$ Dimensional System

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 $d_1\otimes d_2(d_1\le d_2)$ 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.

12 pages, 5 figures, 4 Tables. Accepted in Quantum Information Processing, 2021

References in corpus (7)

• Concurrence of arbitrary dimensional bipartite quantum states
• Quantifying Entanglement with Witness Operators
• A Note on Fully Entangled Fraction
• A family of multipartite separability criteria based on correlation tensor
• Concurrence via entanglement witnesses
• Distance between Bound Entangled States from Unextendible Product Bases and Separable States
• Detection of mixed bipartite entangled state in arbitrary dimension via structural physical approximation of partial transposition

Cited by in corpus (2)

• Physical realization of realignment criteria using structural physical approximation
• Search for an efficient entanglement witness operator for bound entangled states in bipartite quantum systems