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arXiv:0805.4659 · Physical Review A

Induced entanglement enhanced by quantum criticality

Qing Ai, Tao Shi, Guilu Long, C. P. Sun

Published Aug 19, 2008• 31 citations
arXivHTMLPDF

Abstract

Two-qubit entanglement can be induced by a quantum data bus interacting with them. In this paper, with the quantum spin chain in the transverse field as an illustration of the quantum data bus, we show that such induced entanglement can be enhanced by the quantum phase transition (QPT) of the quantum data bus. We consider two external spins simultaneously coupled to a transverse field Ising chain. By adiabatically eliminating the degrees of the chain, the effective coupling between these two spins is obtained. The matrix elements of the effective Hamiltonian are expressed in terms of the dynamical structure factor (DSF) of the chain. The DSF is the Fourier transformation of the Green function of an Ising chain and can be calculated numerically by a method introduced by Derzhko and Krokhmalskii [Phys. Rev. B 56, 11659 (1997)]. Since all characteristics of QPT are embodied in the DSF, the dynamical evolution of the two external spins displays singularity in the vicinity of the critical point.

DOI
10.1103/physreva.78.022327

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Two-qubit entanglement can be induced by a quantum data bus interacting with them. In this paper, with the quantum spin chain in the transverse field as an illustration of the quantum data bus, we show that such induced entanglement can be enhanced by the quantum phase transition (QPT) of the quantum data bus. We consider two external spins simultaneously coupled to a transverse field Ising chain. By adiabatically eliminating the degrees of the chain, the effective coupling between these two spins is obtained. The matrix elements of the effective Hamiltonian are expressed in terms of the dynamical structure factor (DSF) of the chain. The DSF is the Fourier transformation of the Green function of an Ising chain and can be calculated numerically by a method introduced by Derzhko and Krokhmalskii [Phys. Rev. B 56, 11659 (1997)]. Since all characteristics of QPT are embodied in the DSF, the dynamical evolution of the two external spins displays singularity in the vicinity of the critical point.
We study the disentanglement evolution of two spin qubits which interact with a general XYXYXY spin-chain environment. The dynamical process of the disentanglement is numerically and analytically investigated in the vicinity of a quantum phase transition (QPT) of the spin chain in both weak and strong coupling cases. We find that the disentanglement of the two spin qubits may be greatly enhanced by the quantum critical behavior of the environmental spin chain. We give a detailed analysis to facilitate the understanding of the QPT-enhanced decaying behavior of the coherence factor. Furthermore, the scaling behavior in the disentanglement dynamics is also revealed and analyzed.
We study the dynamical process of disentanglement of two qubits and two qutrits coupled to an Ising spin chain in a transverse field, which exhibits a quantum phase transition. We use the concurrence and negativity to quantify entanglement of two qubits and two qutrits, respectively. Explicit connections between the concurrence (negativity) and the decoherence factors are given for two initial states, the pure maximally entangled state and the mixed Werner state. We find that the concurrence and negativity decay exponentially with fourth power of time in the vicinity of the critical point of the environmental system.
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.
Using the method of the Jordan–Wigner transformation for solving different spin–spin correlation functions, we have investigated the generation of next-nearest-neighbouring entanglement in a one-dimensional quantum Ising spin chain with the Gaussian distribution impurities of exchange couplings and external magnetic fields taken into account. The maximal value of entanglement between the next-nearest-neighbouring qubits in the transverse Ising model was analysed in detail by varying the effectively controlled parameters such as interchange coupling, magnetic field and the system impurity. For such systems, where both exchange couplings and external magnetic field disorder appear, we show that it is possible to achieve next-nearest-neighbouring entanglement better than the previously discussed pure Ising spin chain case. We also show that the Gaussian distribution impurity can induce next-nearest-neighbouring entanglement, which can be used as a means to characterize quantum phase transition.
In this paper, we study the dynamical processes of quantum coherence and correlations for two central qubits system coupled with a transverse Ising spin chain. Suppose the initial state of quantum system is the Werner state and the initial state of environment is the ground state of spin chain, and the corresponding time evolution operator, decoherence factor and reduced density matrix are given. We deduce the analytical expressions of evolution of quantum coherence, entanglement and quantum discord. We find that when the spin chain undergoes quantum phase transition (QPT), the entanglement vanished at time [Formula: see text], and the coherence and discord vanished when the decoherence factor decayed to zero. Besides, we also find that the environmental scale N, coupling strength g and parameter P of Werner state do not change the evolution rules of quantum correlation, but accelerate their decay rate with these parameters’ increase.
The disentanglement evolution of bipartite spin- 1 / 2 system coupled to a common surrounding XY chain in transverse fields at nonzero temperature is studied in this letter. The dynamical process of the entanglement is numerically and analytically investigated. We find that thermal effects can enhance disentanglement if the entangled initial state of the central spins does not in the decoherence free space. The critical phenomenon of quantum phase transitions reflected in the disentanglement can be washed out by the thermal effect eventually.