Open-system quantum dynamics with correlated initial states, not completely positive maps, and non-Markovianity
- Department of Physics, Bangalore University, Bangalore-560 056 (India)
- Inspire Institute Inc., Alexandria, Virginia 22303 (United States)
- Department of Physics, Kuvempu University, Shankaraghatta, Shimoga-577 451 (India)
Dynamical A and B maps have been employed extensively by Sudarshan and co-workers to investigate open-system evolution of quantum systems. A canonical structure of the A map is introduced here. It is shown that this canonical A map enables us to investigate whether the dynamics is completely positive (CP) or not completely positive (NCP) in an elegant way and, hence, it subsumes the basic results on open-system dynamics. Identifying memory effects in open-system evolution is gaining increasing importance recently and, here, a criterion of non-Markovianity, based on the relative entropy of the dynamical state is proposed. The relative entropy difference of the dynamical system serves as a complementary characterization--though not related directly--to the fidelity difference criterion proposed recently. Three typical examples of open-system evolution of a qubit, prepared initially in a correlated state with another qubit (environment), and evolving jointly under a specific unitary dynamics--which corresponds to a NCP dynamical map--are investigated by employing both the relative entropy difference and fidelity difference tests of non-Markovianity. The two-qubit initial states are chosen to be (i) a pure entangled state, (ii) the Werner state, which exemplifies both entangled and separable states of qubits, depending on a real parameter, and (iii) a separable mixed state. Both the relative entropy and fidelity criteria offer a nice display of how non-Markovianity manifests itself in all three examples.
- OSTI ID:
- 21537115
- Journal Information:
- Physical Review. A, Vol. 83, Issue 2; Other Information: DOI: 10.1103/PhysRevA.83.022109; (c) 2011 American Institute of Physics; ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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