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Open Physics

Effects of phase shift on bipartite and multipartite correlations of a spin chain under dephasing

Aixi Chen, Jian-Song Zhang

Published Apr 28, 2015• 0 citations
Publisher

Abstract

Abstract We investigate the effects of phase shift on entanglement, quantum discord, geometric discord, and spinsqueezing of a Heisenberg chain under dephasing. An analytical solution of the present model is obtained. Our results show that the initial correlations of the spin chain could be partially stored for a long time in the presence of dephasing and the amount of steady state correlations can be adjusted via phase shift. Particularly, we find the effects of phase shift on quantum discord and geometric discord are not always the same, i.e., the increase of geometric discord does not always imply the increase of quantum discord. Then, we calculate the spin-squeezing of the spin chain and find that spin-squeezing first increases with time and then reaches a plateau. The amount of spin-squeezing can be controlled via phase shift.

DOI
10.1515/phys-2015-0025

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Transmitting quantum states and entanglement through quantum channels is one of the key requirements for the development of quantum computation. Quantum discord has received much attention in quantum computation. We transfer quantum discord through two parallel XXZ spin chains with phase shift. The maximum discord can be enhanced by the phase shift. It will take more time to obtain an enhanced maximum discord in some cases, but for other cases, both the maximum and speed are enhanced by the phase shift. In the thermodynamic limit, the effect of the phase shift disappears and the maximum discord exponentially decays with increasing of the receiving position. Our results on spin chains are generalized to a family of linear Hamiltonians.
We study quantum discord induced by a quantum-critical environment. Two spin halves are independently coupled to the common environment which is modelled by the Ising spin chain in a transverse field. During the time evolution, non-zero discord is induced whereas entanglement cannot be induced due to the special initial state chosen by us. For some cases we analytically obtain quantum discord and its geometric measure. From the numerical results, one can observe that induced quantum discord increases quickly from zero to a steady value when the environment approaches the critical point. Moreover, induced discord may reach its maximum close to the critical point. The special phenomena of induced discord can be used to indicate quantum criticality. We also consider another environment modelled by the spin-1/2 XX chain with three-spin interaction, which also displays second-order quantum phase transition.
Quantum phase transitions of the transverse Ising and antiferromagnetic XXZXXZXXZ spin S=1/2S=1/2S=1/2 chains are studied using quantum discord. Quantum discord allows the measure of quantum correlations present in many-body quantum systems. It is shown that the amount of quantum correlations increases close to the critical points. The observations are in agreement with the information provided by the concurrence, which measures the entanglement of the many-body system.
We study the effect of a phase shift on the amount of transferable two-spin entanglement in a spin chain. We consider a ferromagnetic Heisenberg or XYXYXY spin chain, both numerically and analytically, and two mechanisms to generate a phase shift, the Aharonov-Casher effect, and the Dzyaloshinskii-Moriya interaction. In both cases, the maximum attainable entanglement is shown to be significantly enhanced, suggesting its potential usefulness in quantum information processing.
By using the concept of the quantum discord (QD), we study the spin-1/2 antiferromagnetic Heisenberg chain with next-nearest-neighbor interaction. Due to the SU(2)SU(2)SU(2) symmetry and Z2Z_{2}Z2​ symmetry in this system, we obtain the analytical result of the QD and its geometric measure (GMQD), which is determined by the two-site correlators. For the 4-site and 6-site cases, the connection between GMQD (QD) and the eigenenergies was revealed. From the analytical and numerical results, we find GMQD (QD) is an effective tool in detecting the both the first-order and the infinite-order quantum-phase-transition points for the finite-size systems. Moreover, by using the entanglement excitation energy and a universal frustration measure we consider the frustration properties of the system and find a nonlinear dependence of the GMQD on the frustration.