Master equations for correlated quantum channels.

We derive the general form of a master equation describing the reduced time evolution of a sequence of subsystems "propagating" in an environment which can be described as a sequence of subenvironments. The interaction between subsystems and subenvironments is described in terms of a collision model, with the irreversible dynamics of the subenvironments between collisions explicitly taken into account. In the weak coupling regime, we show that the collisional model produces a correlated Markovian evolution for the joint density matrix of the multipartite system. The associated Lindblad superoperator contains pairwise terms describing cross correlation between the different subsystems. Such a model can describe a broad range of physical situations, ranging from quantum channels with memory to photon propagation in concatenated quantum optical systems.

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

[2]  Vittorio Giovannetti.  A dynamical model for quantum memory channels , 2005 .

[3]  V. Buzek,et al.  Saturation of Coffman–Kundu–Wootters inequalities via quantum homogenization , 2003 .

[4]  M. Horodecki,et al.  Properties of quantum nonsignaling boxes , 2006 .

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

[6]  R. Werner,et al.  Semicausal operations are semilocalizable , 2001, quant-ph/0104027.

[7]  S. Mancini,et al.  Quantum channels with a finite memory , 2003, quant-ph/0305010.

[8]  Stefano Mancini,et al.  Memory effects in attenuation and amplification quantum processes , 2010, 1005.2878.

[9]  R. Xu,et al.  Theory of open quantum systems , 2002 .

[10]  J. Preskill,et al.  Causal and localizable quantum operations , 2001, quant-ph/0102043.

[11]  V. Scarani,et al.  Thermalizing quantum machines: dissipation and entanglement. , 2001, Physical review letters.

[12]  C. Gardiner,et al.  Driving Atoms with Light of Arbitrary Statistics , 1994 .

[13]  Stefano Mancini,et al.  Bosonic memory channels , 2005 .

[14]  C. Macchiavello,et al.  Entanglement-enhanced information transmission over a quantum channel with correlated noise , 2001, quant-ph/0107052.

[15]  R. Werner,et al.  Quantum channels with memory , 2005, quant-ph/0502106.

[16]  Giuliano Benenti,et al.  Enhancement of transmission rates in quantum memory channels with damping. , 2009, Physical review letters.

[17]  Mário Ziman,et al.  Diluting quantum information: An analysis of information transfer in system-reservoir interactions , 2002 .

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

[19]  P. Cochat,et al.  Et al , 2008, Archives de pediatrie : organe officiel de la Societe francaise de pediatrie.

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

[21]  Carmichael,et al.  Quantum trajectory theory for cascaded open systems. , 1993, Physical review letters.

[22]  M B Plenio,et al.  Spin chains and channels with memory. , 2007, Physical review letters.

[23]  V. Giovannetti,et al.  Spin chain model for correlated quantum channels , 2008, 0805.4277.

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

[25]  Mario Ziman,et al.  All (qubit) decoherences: Complete characterization and physical implementation , 2005 .

[26]  C. Macchiavello,et al.  Transition behavior in the channel capacity of two-quibit channels with memory , 2004 .

[27]  Stefano Mancini,et al.  Capacities of lossy bosonic memory channels. , 2009, Physical review letters.

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

[29]  Mário Ziman,et al.  Description of Quantum Dynamics of Open Systems Based on Collision-Like Models , 2004, Open Syst. Inf. Dyn..

[30]  V. Giovannetti,et al.  Teleportation-induced correlated quantum channels. , 2009, Physical review letters.

[31]  S. Virmani,et al.  Many-body physics and the capacity of quantum channels with memory , 2007, 0710.3299.

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

[33]  Gardiner,et al.  Driving a quantum system with the output field from another driven quantum system. , 1993, Physical review letters.

[34]  Giuliano Benenti,et al.  Quantum capacity of dephasing channels with memory , 2007 .

[35]  Reversible and irreversible dynamics of a qubit interacting with a small environment , 2006, quant-ph/0611262.

[36]  R. Gallager.  Information Theory and Reliable Communication , 1968 .