2010/09/30 by Michael J. W. Hall, James D. Cresser, Li Li +1 · 3 citations
Physics and Astronomy · #quant-ph
paper · pdf · doi:10.1103/physreva.89.042120
published as Phys. Rev. A 89, 042120 (2014) · v2: Significant update, with many new results and one new author. 12 pages; v3: Minor clarifications, to appear in PRA; v4: matches published version
arxiv created 2014/05/02 · arxiv updated 2014/05/05
Master equations govern the time evolution of a quantum system interacting with an environment, and may be written in a variety of forms. Time-independent or memoryless master equations, in particular, can be cast in the well-known Lindblad form. Any time-local master equation, Markovian or non-Markovian, may in fact also be written in a Lindblad-like form. A diagonalisation procedure results in a unique, and in this sense canonical, representation of the equation, which may be used to fully characterize the non-Markovianity of the time evolution. Recently, several different measures of non-Markovianity have been presented which reflect, to varying degrees, the appearance of negative decoherence rates in the Lindblad-like form of the master equation. We therefore propose using the negative decoherence rates themselves, as they appear in the canonical form of the master equation, to completely characterize non-Markovianity. The advantages of this are especially apparent when more than one decoherence channel is present. We show that a measure proposed by Rivas et al. is a surprisingly simple function of the canonical decoherence rates, and give an example of a master equation that is non-Markovian for all times t>0, but to which nearly all proposed measures are blind. We also give necessary and sufficient conditions for trace distance and volume measures to witness non-Markovianity, in terms of the Bloch damping matrix.