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arXiv:1511.02473 · Communications in Theoretical Physics

Dynamics of Entanglement in Qubit-Qutrit with x -Component of DM Interaction

Kapil K. Sharma, S.N. Pandey

Published Mar 1, 2016• 17 citations
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Abstract

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 .

DOI
10.1088/0253-6102/65/3/278

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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 .
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 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.
We investigate the dynamics of entanglement for a two-parameter class of states in a hybrid qubit-qutrit system under the influence of various dissipative channels. Our results show that entanglement sudden death (ESD) is a general phenomenon and it usually takes place in a qubit-qutrit system interacting with various noisy channels, not only the case with dephasing and depolarizing channels observed by others. ESD can only be avoided for some initially entangled states under some particular noisy channels. Moreover, the environment affects the entanglement and the coherence of the system in very different ways.
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.
In this paper, we study the entanglement dynamics of two-spin Heisenberg XYZ model with the Dzialoshinskii–Moriya (DM) interaction. The system is initially prepared in the Werner state. The effects of purity of the initial state and DM coupling parameter on the evolution of entanglement are investigated. The necessary and sufficient condition for the appearance of the entanglement sudden death (ESD) phenomenon has been deduced. The result shows that the ESD always occurs if the initial state is sufficiently impure for the given coupling parameter or the DM interaction is sufficiently strong for the given initial state. Moreover, the critical values of them are calculated.