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International Journal of Quantum Information

TRANSMITTING BIPARTITE AND MULTIPARTITE CORRELATIONS VIA SPIN CHAINS UNDER PHASE DECOHERENCE

AI Jian-feng, Jian-Song Zhang, Aixi Chen

Published Sep 1, 2012• 0 citations
Publisher

Abstract

We investigate the transfer of bipartite (measured by cocurrence) and multipartite (measured by global discord) quantum correlations though spin chains under phase decoherence. The influence of phase decoherence and anisotropy parameter upon quantum correlations transfer is investigated. On the one hand, in the case of no phase decoherence, there is no steady state quantum correlations between spins. On the other hand, if the phase decoherence is larger than zero, the bipartite quantum correlations can be transferred through a Heisenberg XXX chain for a long time and there is steady state bipartite entanglement. For a Heisenberg XX chain, bipartite entanglement between two spins is destroyed completely after a long time. Multipartite quantum correlations of all spins are more robust than bipartite quantum correlations. Thus, one can store multipartite quantum correlations in spin chains for a long time under phase decoherence.

DOI
10.1142/s0219749912500736

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We investigate the transfer of bipartite (measured by cocurrence) and multipartite (measured by global discord) quantum correlations though spin chains under phase decoherence. The influence of phase decoherence and anisotropy parameter upon quantum correlations transfer is investigated. On the one hand, in the case of no phase decoherence, there is no steady state quantum correlations between spins. On the other hand, if the phase decoherence is larger than zero, the bipartite quantum correlations can be transferred through a Heisenberg XXX chain for a long time and there is steady state bipartite entanglement. For a Heisenberg XX chain, bipartite entanglement between two spins is destroyed completely after a long time. Multipartite quantum correlations of all spins are more robust than bipartite quantum correlations. Thus, one can store multipartite quantum correlations in spin chains for a long time under phase decoherence.
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.
We study the dynamics of quantum discord and entanglement for two spin qubits coupled to a spin chain with Dzyaloshinsky-Moriya (DM) interaction. We numerically and analytically investigate the time evolution of quantum discord and entanglement for two-qubit initially prepared in a class of X−X-X−structure state. In the case of evolution from a pure state, quantum correlations decay to zero in a very short time at the critical point of the environment. In the case of evolution from a mixed state, It is found that quantum discord may get maximized due to the quantum critical behavior of the environment while entanglement vanishes under the same condition. Moreover, we observed sudden transition between classical and quantum decoherence when single qubit interacts with the environment. The effects of DM interaction on quantum correlations are also considered and revealed in the two cases. It can enhance the decay of quantum correlations and its effect on quantum correlations can be strengthened by anisotropy parameter.
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.
Non-classical correlations arise in various quantum mechanical systems. Characterization and quantification of these correlations is an important and active branch of research in the field of quantum information theory. Investigation of non-classical correlations in condensed matter systems gives important insights about the characteristics of these systems. In particular, systems possessing a quantum critical point in their phase diagrams have attracted much attention due to the peculiar behavior of correlations near these points. In this thesis, we have investigated two distinct quantum spin models from the perspective of correlations and, we have discussed the correlation content of an important subclass of bipartite states. We start by an analytical calculation of the quantum discord for a system composed of spin-j and spin-1/2 subsystems possessing rotational symmetry. We have compared our results with the quantum discord of states having similar symmetries and seen that in rotationally invariant states the amount of quantum discord is much higher. Moreover, using the well known entanglement properties of these states, we have compared their quantum discord with entanglement and seen that quantum discord is higher than the entanglement. Next, we have investigated the thermal quantum correlations and entanglement in spin-1 Bose-Hubbard model with two and three particles. We have demonstrated that the energy level crossings in the ground state of the system are signalled by both the behavior of thermal quantum correlations and entanglement. Finally, we have investigated various thermal quantum and total correlations in the anisotropic XY spin-chain with transverse magnetic field. We have shown that the ability of the considered measures to estimate the critical points of this system at finite temperature strongly depends on the anisotropy parameter of the Hamiltonian. Furthermore, we have studied the effect of temperature on long-range correlations of the XY chain.
Quantum discord is a more general measure of quantum correlations than entanglement and has been proposed as a resource in certain quantum information processing tasks. The computation of discord is mostly confined to two-qubit systems for which an analytical calculational scheme is available. The utilization of quantum correlations in quantum information-based applications is limited by the problem of decoherence, i.e., the loss of coherence due to the inevitable interaction of a quantum system with its environment. The dynamics of quantum correlations due to decoherence may be studied in the Kraus operator formalism for different types of quantum channels representing system-environment interactions. In this review, we describe the salient features of the dynamics of classical and quantum correlations in a two-qubit system under Markovian (memoryless) time evolution. The two-qubit state considered is described by the reduced density matrix obtained from the ground state of a spin model. The models considered include the transverse-field XY model in one dimension, a special case of which is the transverse-field Ising model, and the XXZ spin chain. The quantum channels studied include the amplitude damping, bit-flip, bit-phase-flip and phase-flip channels. The Kraus operator formalism is briefly introduced and the origins of different types of dynamics discussed. One can identify appropriate quantities associated with the dynamics of quantum correlations which provide signatures of quantum phase transitions in the spin models. Experimental observations of the different types of dynamics are also mentioned.
Quantum correlation dynamics in an anisotropic Heisenberg XY Z model under decoherence is investigated by making use of concurrence C and quantum discord(QD).Firstly,we show that both the concurrence and QD exhibit oscillation with time whereas a remarkable difference between them is presented:there is an intermittently sudden phenomenon in the concurrence but not in the QD,which is valid for all the initial states of this system.Also,the interval time of entanglement sudden death is found to be strongly dependent on the initial states,the inhomogeneous magnetic field b and the anisotropic parameter ?.Then,it implies that the steady concurrence and QD can be obtained in the long-time limit,which means that the environmental decoherence cannot entirely destroy the quantum correlation,the variation of the uniform magnetic field B and the anisotropic parameter can change the magnitude of the steady concurrence and QD evidently whereas the parameter b cannot.In addition,based on the analysis of the steady concurrence and QD with t →∞,we give the reason why the magnitude of the steady concurrence and QD is so complicated with the change of the parameters B and △,whereas the parameter b is independent of the steady concurrence and QD.