Non-Markovian random unitary qubit dynamics

Abstract We compare two approaches to non-Markovian quantum evolution: one based on the concept of divisible maps and the other one based on distinguishability of quantum states. The former concept is fully characterized in terms of local generator whereas it is in general not true for the latter one. A simple example of random unitary dynamics of a qubit shows the intricate difference between those approaches. Moreover, in this case both approaches are fully characterized in terms of local decoherence rates.

[1]  S. Luo,et al.  Quantifying non-Markovianity via correlations , 2012 .

[2]  K. Lendi,et al.  Quantum Dynamical Semigroups and Applications , 1987 .

[3]  D. Chru'sci'nski,et al.  Measures of non-Markovianity: Divisibility versus backflow of information , 2011, 1102.4318.

[4]  J Eisert,et al.  Assessing non-Markovian quantum dynamics. , 2007, Physical review letters.

[5]  N. Gisin,et al.  Non-Markovian quantum state diffusion , 1998, quant-ph/9803062.

[6]  E. Sudarshan,et al.  Completely Positive Dynamical Semigroups of N Level Systems , 1976 .

[7]  J. Piilo,et al.  Open system dynamics with non-Markovian quantum jumps , 2009, 0902.3609.

[8]  S. Maniscalco.  Limits in the characteristic-function description of non-Lindblad-type open quantum systems , 2005, quant-ph/0503125.

[9]  H. Breuer,et al.  Structure of completely positive quantum master equations with memory kernel. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Dariusz Chruściński,et al.  Non-Markovian quantum dynamics: local versus nonlocal. , 2009, Physical review letters.

[11]  Francesco Petruccione,et al.  Non-Markovian dynamics of a qubit , 2006 .

[12]  Bassano Vacchini,et al.  Quantum semi-Markov processes. , 2008, Physical review letters.

[13]  Erika Andersson,et al.  Revival of quantum correlations without system-environment back-action , 2010, 1009.5710.

[14]  Sabrina Maniscalco,et al.  Complete positivity of a spin-1/2 master equation with memory , 2007 .

[15]  C. P. Sun,et al.  Quantum Fisher information flow and non-Markovian processes of open systems , 2009, 0912.0587.

[16]  Nicolas Gisin,et al.  Open system dynamics with non-markovian quantum trajectories , 1999 .

[17]  Completely positive post-Markovian master equation via a measurement approach , 2004, quant-ph/0404077.

[18]  G. Lindblad.  On the generators of quantum dynamical semigroups , 1976 .

[19]  Jyrki Piilo,et al.  Non-Markovian quantum jumps. , 2007, Physical review letters.

[20]  M. Paternostro,et al.  Memory-keeping effects and forgetfulness in the dynamics of a qubit coupled to a spin chain , 2010, 1011.5653.

[21]  J. Cirac,et al.  Dividing Quantum Channels , 2006, math-ph/0611057.

[22]  Bassano Vacchini,et al.  A classical appraisal of quantum definitions of non-Markovian dynamics , 2012, 1207.3918.

[23]  Susana F Huelga,et al.  Entanglement and non-markovianity of quantum evolutions. , 2009, Physical review letters.

[24]  Francesco Petruccione,et al.  The Theory of Open Quantum Systems , 2002 .

[25]  Maria Mannone,et al.  Comparison of non-Markovianity criteria in a qubit system under random external fields , 2012, 1209.6331.

[26]  A. Rajagopal,et al.  Kraus representation of quantum evolution and fidelity as manifestations of Markovian and non-Markovian forms , 2010, 1007.4498.

[27]  C. H. Oh,et al.  Alternative non-Markovianity measure by divisibility of dynamical maps , 2011, 1102.4659.

[28]  Krzysztof Wódkiewicz,et al.  Depolarizing channel as a completely positive map with memory , 2004 .

[29]  Jyrki Piilo,et al.  Measure for the degree of non-markovian behavior of quantum processes in open systems. , 2009, Physical review letters.

[30]  Sudha,et al.  Interplay of Quantum Stochastic and Dynamical Maps to Discern Markovian and Non-Markovian Transitions , 2012, 1201.0477.

[31]  X. Yi,et al.  Singularity of dynamical maps , 2012, 1203.0053.

[32]  Elsi-Mari Laine,et al.  Markovianity and non-Markovianity in quantum and classical systems , 2011, 1106.0138.

[33]  Andrzej Kossakowski,et al.  Markovianity criteria for quantum evolution , 2012, 1201.5987.

[34]  J. Cresser,et al.  Comparing different non-Markovianity measures in a driven qubit system , 2010, 1011.5328.

[35]  D. Chruściński,et al.  Witnessing non-Markovianity of quantum evolution , 2012, 1210.8079.

[36]  G. Guo,et al.  Experimental control of the transition from Markovian to non-Markovian dynamics of open quantum systems , 2011, 1109.2677.

[37]  S. Maniscalco,et al.  DYNAMICS OF QUANTUM CORRELATIONS IN TWO-QUBIT SYSTEMS WITHIN NON-MARKOVIAN ENVIRONMENTS , 2012, 1205.6419.