Bound entangled Bell diagonal states of unequal local dimensions, and their witnesses

TL;DR

This paper generalizes Bell diagonal states to unequal local dimensions, develops entanglement witnesses for these states, and constructs bound entangled states undetected by common criteria, advancing quantum entanglement detection methods.

Contribution

It introduces a generalized class of Bell diagonal states with unequal local dimensions and extends entanglement witnesses to non-Hermitian bases, improving detection of bound entanglement.

Findings

Extended entanglement criteria to non-Hermitian bases

Constructed bound entangled states undetected by standard criteria

Optimized witnesses for noise robustness

Abstract

Bell diagonal states constitute a well-studied family of bipartite quantum states that arise naturally in various contexts in quantum information. In this paper we generalize the notion of Bell diagonal states to the case of unequal local dimensions and investigate their entanglement properties. We extend the family of entanglement criteria of Sarbicki et al. to non-Hermitian operator bases to construct entanglement witnesses for the class of generalized Bell diagonal states. We then show how to optimize the witnesses with respect to noise robustness. Finally, we use these witnesses to construct bound entangled states that are not detected by the usual computable cross norm or realignment and de Vicente criteria.