BIPARTITE AND MULTIPARTITE CORRELATIONS OF COUPLED QUBITS IN A NON-MARKOVIAN ENVIRONMENT: HIERARCHY EQUATION METHOD

We study bipartite and multipartite correlations of several coupled qubits within a common non-Markovian bath using the hierarchy equation method. This method does not use the rotating-wave and Born–Markovian approximations. The interaction between the qubits and their coupling strength with the bath have remarkable influence on the dynamics of quantum correlations. The entanglement sudden death (ESD) phenomenon, the amount of stationary state concurrence and spin squeezing can be controled by the non-Markovianity of the environment and interactions between qubits. These properties may be useful for purposes of quantum information processing with multiqubit system in non-Markovian environments.

The Advantages of Not Entangling Macroscopic Diamonds at Room Temperature

The recent paper entitled by K. C. Lee et al. (2011) establishes nonlocal macroscopic quantum correlations, which they term “entanglement”, under ambient conditions. Photon(s)-phonon entanglements are established within each interferometer arm. However, our analysis demonstrates, the phonon fields between arms become correlated as a result of single-photon wavepacket path indistinguishability, not true nonlocal entanglement. We also note that a coherence expansion (as opposed to decoherence) resulted from local entanglement which was not recognized. It occurred from nearly identical Raman scattering in each arm (importantly not meeting the Born and Markovian approximations). The ability to establish nonlocal macroscopic quantum correlations through path indistinguishability rather than entanglement offers the opportunity to greatly expand quantum macroscopic theory and application, even though it was not true nonlocal entanglement.

Mean-field evolution of open quantum systems: an exactly solvable model

We consider quantum particles coupled to local and collective thermal quantum environments. The coupling is energy conserving, and the collective coupling is scaled in the mean-field way. There is no direct interaction between the particles. We show that an initially factorized state of the particles remains factorized at all times, in the limit of large particle number. Each single-particle factor evolves according to an explicit, nonlinear, dissipative and time-dependent Hartree–Lindblad equation. The model is exactly solvable; we do not make any weak coupling or any Markovian approximations, and our results are mathematically rigorous.

QUANTUM MARKOVIAN APPROXIMATIONS FOR FERMIONIC RESERVOIRS

We establish a quantum functional central limit for the dynamics of a system coupled to a fermionic bath with a general interaction linear in the creation, annihilation and scattering of the bath reservoir. Following a quantum Markovian limit, we realize the open dynamical evolution of the system as an adapted quantum stochastic process driven by fermionic noise.

Near Complete Decomposability: Bounding the Error by a Stochastic Comparison Method

An aggregation technique of ‘near complete decomposable' Markovian systems has been proposed by Courtois [3]. It is an approximate method in many cases, except for some queuing networks, so the error between the exact and the approximate solution is an important problem. We know that the error is O(ε), where ε is defined as the maximum coupling between aggregates. Some authors developed techniques to obtain a O(ε k) error with k > 1 error with k > 1, while others developed a technique called ‘bounded aggregation’. All these techniques use linear algebra tools and do not utilize the fact that the steady-state probability vector represents the distribution of a random variable. In this work we propose a stochastic approach and we give a method to obtain stochastic bounds on all possible Markovian approximations of the two main dynamics: short-term and long-term dynamics.

Near Complete Decomposability: Bounding the Error by a Stochastic Comparison Method

An aggregation technique of ‘near complete decomposable' Markovian systems has been proposed by Courtois [3]. It is an approximate method in many cases, except for some queuing networks, so the error between the exact and the approximate solution is an important problem. We know that the error is O(ε), where ε is defined as the maximum coupling between aggregates. Some authors developed techniques to obtain a O(ε k ) error with k > 1 error with k > 1, while others developed a technique called ‘bounded aggregation’. All these techniques use linear algebra tools and do not utilize the fact that the steady-state probability vector represents the distribution of a random variable. In this work we propose a stochastic approach and we give a method to obtain stochastic bounds on all possible Markovian approximations of the two main dynamics: short-term and long-term dynamics.