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Open Systems & Information Dynamics

On Symmetric Bound Entangled States of Two Qudits

Dariusz Chruściński, Takashi Matsuoka, Tatsunori Saito, Yuji Hirota, Masanari Asano

Published Nov 25, 2013• 1 citation
Publisher

Abstract

We provide a symmetric class of 2-qudit bound entangled states within a so-called magic simplex of Bell diagonal states. This class generalizes well-known family of 2-qutrit states introduced by Horodecki.
DOI
10.1142/s1230161213500133

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The concept of symmetric extendibility has recently drawn attention in the context of tolerable error rates in quantum cryptography, where it can be used to decide whether quantum states shared between two parties can be purified by means of entanglement purification with one-way classical communication only. Unfortunately, at present there exists no simple general criterion to decide whether a state possesses a symmetric extension or not. In this paper, we derive criteria for symmetric extendibility within subclasses of all two-qudit states. Using these criteria, we can completely solve the problem for a two-parameter family of two-qudit states, which includes the isotropic states as a subclass.
Abstract. The concept of symmetric extendibility has recently drawn attention in the context of tolerable error rates in quantum cryptography, where it can be used to decide whether quantum states shared between two parties can be purified by means of entanglement purification with one-way classical communication only. Unfortunately, at present there exists no simple general criterion to decide whether a state possesses a symmetric extension or not. In this article we derive criteria for symmetric extendibility within subclasses of all two-qudit states. Using these criteria, we can completely solve the problem for a two-parameter family of two-qudit states, which includes the isotropic states as a subclass. PACS numbers: 03.67.-a, 03.67.Dd, 03.67.HkSymmetric extendibility for a class of qudit states 2 1.