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

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.

11 pages, 5 figures, 1 table; added examples in sections 2 and 5

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Cited by in corpus (5)

• Bipartite Bound Entanglement
• Real randomized measurements for analyzing properties of quantum states
• Group-Theoretic Perspective on the PPT and Realignment Criteria in the Magic Simplex for Bipartite Qutrits
• Bound entanglement-assisted prepare-and-measure scenarios based on four-dimensional quantum messages
• Bound entanglement in symmetric random induced states