Geometric discord and Measurement-induced nonlocality for well known bound entangled states

TL;DR

This paper quantifies non-classical correlations in well-known bound entangled states using geometric discord and measurement-induced nonlocality, revealing consistent measures across different state families and dimensions.

Contribution

It provides analytical results for non-classical correlations in various bound entangled states, highlighting their similarities across different state classes and dimensions.

Findings

Measures are mostly analytic and small in value.

Same quantumness in certain bound entangled states with different dimensions.

Werner and isotropic states show similar properties when viewed in specific dimensions.

Abstract

We employ geometric discord and measurement induced nonlocality to quantify non classical correlations of some well-known bipartite bound entangled states, namely the two families of Horodecki's ($2\otimes 4$, $3\otimes 3$ and $4\otimes 4$ dimensional) bound entangled states and that of Bennett etal's in $3\otimes 3$ dimension. In most of the cases our results are analytic and both the measures attain relatively small value. The amount of quantumness in the $4\otimes 4$ bound entangled state of Benatti etal and the $2\otimes 8$ state having the same matrix representation (in computational basis) is same. Coincidently, the $2m\otimes 2m$ Werner and isotropic states also exhibit the same property, when seen as $2\otimes 2m^2$ dimensional states.