Non-Markovian evolution of quantum systems (量子科学における双対性とスケール)

Sonja Daffer

Ying-Jie Zhang, Yun‐Jie Xia, Heng Fan

We illustrate a scheme for implementing a non-Markovian speedup evolution of an open system weakly interacting with a controllable environment: the coupled qubit-array. By controlling the environment, for instance by choosing a judicious nearest-neighbor excitation quanta hopping strength among the qubit-array or by changing the number of qubits coupled to the quantum system, two dynamical crossovers from Markovian to non-Markovian and from no-speedup to speedup are achieved in the weak system-environment coupling regime. For the weaker system-environment coupling, the larger hopping strength (or the larger qubits number) should be tuned to drive the non-Markovian speedup evolution. Particularly, the controllable non-Markovian dynamics is the intrinsic physical reason for the speedup evolution of a quantum system.

Dariusz Chruściński, Andrzej Kossakowski

Doyeol Ahn, Jinhyoung Lee, M. S. Kim +1 more

We study non-Markovian decoherence phenomena by employing projection-operator formalism when a quantum system (a quantum bit or a register of quantum bits) is coupled to a reservoir. By projecting out the degree of freedom of the reservoir, we derive a non-Markovian master equation for the system, which is reduced to a Lindblad master equation in Markovian limit, and obtain the operator sum representation for the time evolution. It is found that the system is decohered slower in the non-Markovian reservoir than the Markovian because the quantum information of the system is memorized in the non-Markovian reservoir. We discuss the potential importance of non-Markovian reservoirs for quantum-information processing.

Dariusz Chruściński

A. K. Rajagopal, A. R. Usha Devi, R. W. Rendell

It is shown that the fidelity of the dynamically evolved system with its earlier time-density matrix provides a signature of non-Markovian dynamics. Also, the fidelity associated with the initial state and the dynamically evolved state is shown to be larger in the non-Markovian evolution compared to that in the corresponding Markovian case. Starting from the Kraus representation of quantum evolution, the Markovian and non-Markovian features are discerned in its short-time structure. These two features are in concordance with each other and they are illustrated with the help of four models of interaction of the system with its environment.