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Open Systems & Information Dynamics

A Class of Bound Entangled States of Two Qutrits

Jacek Jurkowski, Dariusz Chruściński, A. Rutkowski

Published Aug 13, 2009• 10 citations
Publisher

Abstract

We provide a new class of states of two qutrits displaying the so-called bound entanglement. We investigate the states using various versions of computable cross-norm and realignment criteria recently introduced in [7].
DOI
10.1142/s1230161209000177

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We consider a tripartite system of a non-interacting qutrit pair and one enviornmental qutrit which interact with any one of the qutrit of the pair through Dzyaloshinskii-Moriya (DM) interaction. The purpose of this study is to show that DM interaction convert bound entangled states to free entangled states, which are easily distillable. Here we take two qutrit bound entangled states investigated by Jurkowski \textit{et al.} [Open Sys. Info. Dynamics, Vol 16, pp. 235-242, 2009]. It is also interesting to note that probability amplitude of environmental qutrit do not play any role in free entanglement conversion. In this work we have used the computable cross norm realignment criteria to detect the bound entanglement, and negativity have been used to measure free entanglement. We also investigate the distillability sudden death and its possibility in the two qutrits system.
In this article we investigate the role of Dzyaloshinskii-Moriya (DM) interaction as a useful resource to distil the bound entanglement in two qutrits. Here we study the distillability of Jurkowski et al. bound entangled states. We consider the close system of two qutrits prepared initially in bound entangled states and an auxiliary qutrit prepared in pure state. The auxiliary qutrit interacts with any one of the qutrit of the closed system through DM interaction. The composite system evolve under unitary dynamics. Taking the partial trace operation over the auxiliary qutrit, we show the distillability of Jurkowski et al. bound entangled states under DM interaction. It is interesting to investigate that probability amplitude of auxiliary qutrit do not play the role in dynamics, while DM interaction strength is responsible to free the bound entangled states, which can be further distilled. In this work we have used the computable cross norm realignment criteria to detect the bound entanglement and negativity have been used to measure the free entanglement.
Entanglement is a key feature in many quantum technologies, including secure communication protocols and quantum computing. However, detecting it in mixed quantum states remains a challenging task. While the positive partial transposition (PPT) and computable cross-norm and realignment criteria are well-established tools for entanglement detection in general, and are especially effective in Bell-diagonal states, their connection to the underlying group structure of this state family has not been fully explored. In this work, we analyze the PPT and realignment criteria for Bell-diagonal states from a group-theoretic point of view. Our results demonstrate that the group structure of Bell-diagonal states provides a clear framework for analyzing and computing these two entanglement-detection criteria, thereby highlighting the connection between entanglement and group structure. This unified perspective offers insights into the mathematical and physical properties of entanglement in structured quantum systems and ties the PPT and realignment criteria for Bell-diagonal states to experimental procedures.