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arXiv:1509.01001

Dynamic Entanglement Evolution of Two-qubit XYZ Spin Chain in Markovian Environment

Ren Yi-Chong, Fan Hong-Yi

Published Sep 3, 2015• 0 citations
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Abstract

We propose a new approach called Ket-Bra Entangled State (KBES) Method for converting master equation into Schrödinger-like equation. With this method, we investigate decoherence process and entanglement dynamics induced by a $2$-qubit spin chain that each qubit coupled with reservoir. The spin chain is an anisotropy $XYZ$ Heisenberg model in the external magnetic field $B$, the corresponding master equation is solved concisely by KBES method; Furthermore, the effects of anisotropy, temperature, external field and initial state on concurrence dynamics is analyzed in detail for the case that initial state is Extended Wenger-Like(EWL) state. Finally we research the coherence and concurrence of the final state (namely the density operator for time tend to infinite)

DOI
10.48550/arxiv.1509.01001

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We propose a new approach called Ket-Bra Entangled State (KBES) Method for converting master equation into Schrödinger-like equation. With this method, we investigate decoherence process and entanglement dynamics induced by a 222-qubit spin chain that each qubit coupled with reservoir. The spin chain is an anisotropy XYZXYZXYZ Heisenberg model in the external magnetic field BBB, the corresponding master equation is solved concisely by KBES method; Furthermore, the effects of anisotropy, temperature, external field and initial state on concurrence dynamics is analyzed in detail for the case that initial state is Extended Wenger-Like(EWL) state. Finally we research the coherence and concurrence of the final state (namely the density operator for time tend to infinite)
Taking the decoherence effect into account, the entanglement evolution of a two-qubit anisotropic Heisenberg XYZ chain in the presence of inhomogeneous magnetic field is investigated. The time evolution of concurrence is studied for the initial state cos θ |01⟩ +sin θ|10⟩ at zero temperature. The influences of inhomogeneous magnetic field, anisotropic parameter and decoherence on entanglement dynamic are addressed in detail, and a concurrence formula of the steady state is found. It is shown that the entanglement sudden death (ESD) and entanglement sudden birth (ESB) appear with the decoherence effect, and the stable concurrence depends on the uniform magnetic field B , anisotropic parameter Δ and environment coupling strength γ, which is independent of different initial states and nonuniform magnetic field b.
The exact quantum dynamics of the reduced density matrix of two coupled spin qubits in a quantum Heisenberg XYXYXY spin star environment in the thermodynamic limit at arbitrarily finite temperatures is obtained using an operator technique. In this approach, the transformed Hamiltonian becomes effectively Jaynes-Cumming-like and thus the analysis is also relevant to cavity quantum electrodynamics. This special operator technique is mathematically simple and physically clear, and allows us to treat systems and environments that could all be strongly coupled mutually and internally. To study their entanglement evolution, the concurrence of the reduced density matrix of the two coupled central spins is also obtained exactly. It is shown that the dynamics of the entanglement depends on the initial state of the system and the coupling strength between the two coupled central spins, the thermal temperature of the spin environment, and the interaction between the constituents of the spin environment. We also investigate the effect of detuning, which in our model can be controlled by the strength of a locally applied external magnetic field. It is found that the detuning has a significant effect on the entanglement generation between the two-spin qubits.
This paper investigates the entanglement evolution of a two-qubit anisotropic Heisenberg XYZ chain in the presence of Dzyaloshinskii–Moriya interaction. The time evolution of the concurrence is studied for the initial pure entangled states cos θ |00⟩ + sin θ |11⟩ and cos φ |01⟩ + sin φ |10⟩ at zero temperature. The influences of Dzyaloshinskii–Moriya interaction D , anisotropic parameter Δ and environment coupling strength γ on entanglement evolution are analysed in detail. It is found that the effect of noisy environment obviously suppresses the entanglement evolution, and the Dzyaloshinskii–Moriya interaction D acts on the time evolution of entanglement only when the initial state is cos φ |01⟩ + sin φ |10⟩. Finally, a formula of steady state concurrence is obtained, and it is shown that the stable concurrence, which is independent of different initial states and Dzyaloshinskii–Moriya interaction D , depends on the anisotropic parameter Δ and the environment coupling strength γ.
By analytically solving the Lindblad form of the master equation, we investigate entanglement dynamics of two qubits coupled via the XY interaction, where each qubit is interacting with an independent reservoir with the squeezing parameters and squeezing angles. In the weak-squeezed reservoir, we show that the entanglement sudden death and entanglement sudden birth will happen for various entangled states. Some initial product states evolve into entangled ones, initially entangled states lose completely or partially their entanglement. The effects of varying the degree of entanglement of the initial states, the spin chain system parameters and different values of the degree of squeezing on the sudden death, revival and birth times are analyzed in detail. We also see that the steady state concurrence appears in the squeezed dissipative environments, which is affected by both the system parameters and the degree of squeezing.