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Distillation of a Bound Entangled State Under the Influence of Different Interactions

Suprabhat Sinha

Published Oct 14, 2021• 0 citations
OpenAlex

Abstract

In this article, the dynamics of an open quantum system is investigated for one of the bound entangled states proposed by Bennett et al. under the influence of Heisenberg interaction, bi-linear bi-quadratic interaction, and Dzyaloshinskii-Moriya (DM) interaction. During the study, one qutrit of the selected two qutrit bound entangled state has interacted with an auxiliary qutrit through different interactions. It is observed that, although the auxiliary qutrit plays a significant role during the interaction, the probability amplitude of the qutrit does not affect the open quantum system. In the present work, the computable cross-norm or realignment (CCNR) criterion has been used to detect the bound entanglement of the state and the negativity has been applied to measure the free entanglement. In this three-fold study, it is found that the bi-linear bi-quadratic interaction performs better to free the bound entanglement.

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In this article, the dynamics of an open quantum system is investigated for one of the bound entangled states proposed by Bennett et al. under the influence of Heisenberg interaction, bi-linear bi-quadratic interaction, and Dzyaloshinskii-Moriya (DM) interaction. During the study, one qutrit of the selected two qutrit bound entangled state has interacted with an auxiliary qutrit through different interactions. It is observed that, although the auxiliary qutrit plays a significant role during the interaction, the probability amplitude of the qutrit does not affect the open quantum system. In the present work, the computable cross-norm or realignment (CCNR) criterion has been used to detect the bound entanglement of the state and the negativity has been applied to measure the free entanglement. In this three-fold study, it is found that the bi-linear bi-quadratic interaction performs better to free the bound entanglement.
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.
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.
Abstract In this present paper, we study the entanglement dynamics in qubit A-qutrit B pair under x component of Dzyaloshinshkii–Moriya interaction (D x ) by taking an auxiliary qubit C. Here, we consider an entangled qubit-qutrit pair initially prepared in two parameter qubit-qutrit states and one auxiliary qubit prepared in pure state interacts with the qutrit of the pair through DM interaction. We trace away the auxiliary qubit and calculate the reduced dynamics in qubit A-qutrit B pair to study the influence of the state of auxiliary qubit C and D x on entanglement. We find that the state (probability amplitude) of auxiliary qubit does not influence the entanglement, only D x influences the same. The phenomenon of entanglement sudden death (ESD) induced by D x has also been observed. We also present the affected and unaffected two parameter qubit-qutrit states by D x .
The effect of stochastic dephasing on the dynamics of entanglement of qutrit-qutrit states is investigated by using negativity and bound entanglement defined with realignment criterion. From the analysis, we find that the time evolution of quantum free entanglement and bound entanglement depends on the fluctuations of the stochastic variables and the parameters of the particular initial states of concern. Our results imply that some qutrits states display both distillability sudden death and entanglement sudden death, while some states do not display distillability sudden death but only entanglement sudden death.
Entanglement dynamics of a qutrit-qutrit system under the influence of global, local and multilocal decoherence introduced by phase flip, trit flip and trit phase flip channels is investigated. The negativity and realignment criterion are used to quantify the entanglement of the system. It is shown that the entanglement sudden death and distibility sudden death can be avoided in the presence of phase flip, trit flip and trit-phase flip environments. It is shown that certain free entangled distillable qutrit states become bound entangled or separable i.e. convert into non-distillable states under different flipping noises. It is also seen that local operations do not have any effect on the entanglement dynamics of the system. Further more, no ESD and DSD is seen for the case of trit flip channel.
The dynamics of distillability entanglement between qutrit—qutrit systems interacting with a thermal reservoir is investigated in this paper. We discovered an interesting phenomenon that under a thermal reservoir certain initially prepared free-entangled states become bound-entangled states in a finite time, which is called distillability sudden death (DSD). We use a realignment criterion to measure the nine-dimensional density matrix of the entanglement. Moreover, we analyze some other parameters to investigate the effects to the systems. Explanations are then given.