arXiv:2406.11205 · Open Systems & Information Dynamics

CP Conditions for GKSL-Like Master Equations

Akane Watanabe, Makoto Unoki, Hiromichi Nakazato, Takayuki Suzuki

Published Dec 1, 2024• 1 citation

Abstract

Complete positivity (CP) of a quantum dynamical map (QDM) is, in general, difficult to show when its master equation (ME) does not conform to the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) form. The GKSL ME describes Markovian dynamics, comprising a unitary component with time-independent Hermitian operators and a nonunitary component with time-independent Lindblad operators and positive time-independent damping rates. Recently, non-Markovian dynamics have received growing attention, and the various types of GKSL-like MEs with time-dependent operators are widely discussed; however, rigorous discussions on their CP conditions remain limited. This paper presents conditions for QDMs to be CP, whose MEs take the GKSL-like form with arbitrary time dependence. One case considered is where its ME takes the time-local integro-differential GKSL-like form, which includes CP-divisible cases. Another case considered is where the ME is time-non-local but can be approximated to be time-local in the weak-coupling regime. As a special case of the time-non-local case, the same discussion holds for the time-convoluted GKSL-like form, which should be compared to previous studies.

DOI: 10.1142/s1230161224500173

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