A mirrored pair of optimal non-decomposable entanglement witnesses for two qudits does exist

Abstract

Two approaches can be utilized to handle the separability problem, finding out whether a given bipartite qudit state is separable or not: a direct procedure on the state space or the effective tool of entanglement witnesses (EWs). This contribution studies the structure of EWs. Exploiting the very concept of mirrored EWs, increasing the detection power, we show, in contrast to the conjecture in a recent paper (Sci. Rep. {\bf 13}, 10733 (2023)), there exist pairs of optimal EWs, which are both non-decomposible, i.e. can detect bound/PPT-entangled states in an optimal way. Since we show that the structure also extends to higher dimensions, our results reveal a further structure of entanglement witnesses.

14 pages, 4 figues

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Cited by in corpus (2)

• Mirrored Entanglement Witnesses for Multipartite and High-Dimensional Quantum Systems
• Spectral characterizations of entanglement witnesses