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Distillation of bound entanglement through Dzyaloshinskii-Moriya interaction

Kapil K. Sharma

Published Dec 16, 2014• 0 citations
OpenAlex

Abstract

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.

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•May 27, 2014•0 citations
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.
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.
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 .
Recently, Mazhar Ali ( Phys. Rev. A , 81 (2010) 042303 and J. Phys. B , 43 (2010) 045504) showed the phenomenon of distillability sudden death (DSD) in qutrit-qutrit systems under amplitude damping. In this paper, the phenomenon of distillability sudden death in two-qutrit systems which are in the presence of the external magnetic field and Dzyaloshinskii-Moriya (DM) interaction under decoherence has been investigated. With the help of the realignment criterion, we show that certain initial prepared free entangled states may become bound entangled states in a finite time. Moreover, the effects of the external magnetic field strength and the DM interaction parameter, as well as the intrinsic decoherence parameter on the possibility of DSD in our model have been studied in detail.
In this article, we present the entanglement dynamics in a qubit-qutrit system. Here, we consider a closed system as a pair of qubit-qutrit and an external qubit which interacts with the qutrit of the closed system via y-component of the Dzyaloshinskii-Moriya (DM) interaction. We find that the state of external qubit do not affect the entanglement in two parameter qubit-qutrit states, it is only DM interaction strength which is affecting the entanglement. Further, we investigate the phenomenon of entanglement sudden death and identify the affected and unaffected two parameter qubitqutrit states by DM interaction.
We investigate the exact entanglement dynamics of a two-qubit Heisenberg XXZ chain with Dzyaloshinskii-Moriya (DM) interactions, interacting with an anisotropic spin bath in thermal equi- librium at a temperature T, driven by an external magnetic field B along the z-axis. We establish that, for an initially entangled qubit pair, the DM interactions generate entanglement and enhance the entanglement in the revival region. The effects of the DM interaction are also seen to be very important at high temperatures and for weak coupling between the two qubits where it is seen to preserve entanglement. These effects are weakened when the magnetic field B and the Heisenberg coupling are switched on. If the two-qubits are prepared in an initially separable state, the DM in- teraction instead has a negative effect on their entanglement. On a whole entanglement can better be preserve in the spin chain even at high temperatures by increases the external magnetic field B and the Heisenberg couplings, and by tuning the strength of the DM interaction.