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Journal of Physics A Mathematical and Theoretical

A relaxation process including interaction effects of a two-qubit system

Masashi Ban

Published Dec 17, 2009• 5 citations
Publisher

Abstract

A relaxation process of a two-qubit system is studied by means of the quantum master equation.The two qubits interact with each other via the Ising-type coupling, and one of the two qubits is placed under the influence of a thermal reservoir and the other is isolated from an environmental system.It is shown that the interaction between the two qubits significantly affects the relaxation process.The synthetic effect of the interaction between the qubit-qubit interaction and qubit-reservoir interaction induces the entanglement suddenbirth and the violation of the Bell inequality, even if there is no entanglement in an initial state of the two qubits.

DOI
10.1088/1751-8113/43/3/035303

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A relaxation process of a two-qubit system is studied by means of the quantum master equation.The two qubits interact with each other via the Ising-type coupling, and one of the two qubits is placed under the influence of a thermal reservoir and the other is isolated from an environmental system.It is shown that the interaction between the two qubits significantly affects the relaxation process.The synthetic effect of the interaction between the qubit-qubit interaction and qubit-reservoir interaction induces the entanglement suddenbirth and the violation of the Bell inequality, even if there is no entanglement in an initial state of the two qubits.
A phase relaxation process of interacting two qubits is studied by means of the quantum master equation, where each qubit is influenced by an independent thermal reservoir. The damping operator of the quantum master equation consists of two parts; one includes the effects of the interaction between the qubits and the other does not. It is shown that the interaction significantly affects the phase relaxation process. The decoherence of entanglement is investigated for the two qubits initially prepared in the XXX state.
We investigate a system of two interacting qubits having one of them isolated and the other coupled to a thermal reservoir. We consider two different models of system-reservoir interaction: i) a model, in which the master equation is derived taking into account the interaction between the two subsystems (qubits), ii) a naive model, in which the master equation consists of a dissipative term added to the unitary evolution term. We study the dynamics of quantities such as bipartite entanglement, quantum discord and the linear entropy of the isolated qubit for both strong and weak coupling regimes (qubit-qubit interaction) as well as for different temperatures of the reservoir. We find significant disagreements between the results obtained from the two models even in the weak coupling regime. For instance, we show that according to the phenomenological model, the isolated qubit would approach a maximally mixed state more slowly for higher temperatures (unphysical result), while the microscopic model predicts the opposite behaviour (correct result).
The decoherence of entanglement of two-qubit states is investigated by means of the non-Markovian quantum master equation. It is assumed that the decoherence is caused by environmental systems in non-stationary states, which evolve from initial states into equilibrium states. In this case, the non-Markovian nature of the environmental systems is of essential importance. It is shown that the disentanglement time after which there is no qubit entanglement is determined by the non-Markovian effect and the thermal effect of the environmental systems.
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.
In a two-qubit system the coupling with an environment considerably affects the entanglement dynamics, usually leads to the loss of entanglement within a finite time. Since entanglement is a key feature in the application of such systems to quantum information processing, it is highly desirable to find a way to prolonging its lifetime. We present a simple model of an interacting two-qubit system in the presence of a thermal Markovian environment. The qubits are modeled as interacting spin-1∕21∕21∕2 particles in a magnetic field and the environment is limited to inducing single spin-flip events. A simple scheme allows us to calculate the relaxation rates for all processes. We show that the relaxation dynamics of the most entangled state exhibit critical slowing down as a function of the magnetic field, where the relaxation rate changes from exponentially small values to finite values in the zero-temperature limit. We study the effect of temperature and magnetic field on all the other relaxation rates and find that they exhibit unusual properties, such as nonmonotonic dependence on temperature and a discontinuity as a function of magnetic field. In addition, a simple scheme to include non-Markovian effects is presented and applied to the two-qubit model. We find that the relaxation rates exhibit a sharp, cusplike resonant structure as a function of the environment memory time, and that for long memory times all the different relaxation rates merge into a single one.
Time evolution of a quantum system which is influenced by a stochastically fluctuating environment is studied by means of the stochastic Liouville equation. The two different types of the stochastic Liouville equation and their relation are discussed. The stochastic Liouville equation is shown to be derived from the quantum master equation of the Lindblad under certain conditions. Relaxation processes of single and bipartite quantum systems which are initially correlated with a stochastic environment are investigated. It is shown the possibility that the stochastic fluctuation can create coherence and entanglement of a quantum system with the assistance of the initial correlation. The results are examined in the pure dephasing processes of qubits, which are caused by the nonstationary Gauss-Markov process and two-state jump Markov process.