Invertibility as a witness of Markovianity of the quantum dynamical maps
arXiv:2012.08360 · doi:10.1007/s13538-023-01274-0
Abstract
Markovianity of the quantum open system processes is a topic of the considerable current interest. Typically, invertibility is assumed to be non-essential for Markovianity of the open-quantum-system dynamical maps. Nevertheless, in this paper we distinguish a class of physically important dynamical maps (processes) for which invertibility is a necessary condition for Markovianity. Since every quantum-state tomography directly provides information on invertibility of the map, no optimization procedure is necessary for determining non-Markovianity regarding the considered class of dynamical processes. On this basis we are able to provide a systematic insight and to distinguish mutual relations of the various approaches to quantum Markovianity. Notably, for the processes out of the considered class of dynamical maps, various relations are allowed between divisibility, invertibility and Markovianity of the dynamical maps.
20 pages, 1 figure, discussion extended, new references, Supplementary material added
References in corpus (14)
- Quantum Non-Markovianity: Characterization, Quantification and Detection
- Vanishing quantum discord is necessary and sufficient for completely positive maps
- Operational Markov condition for quantum processes
- On measures of non-Markovianity: divisibility vs. backflow of information
- Quantum stochastic processes and quantum non-Markovian phenomena
- Finding the Kraus decomposition from a master equation and vice versa
- Vanishing quantum discord is not necessary for completely-positive maps
- Temporal self-similarity of quantum dynamical maps as a concept of memorylessness
- Tensor power of dynamical maps and P- vs. CP-divisibility
- Convex Combinations of Pauli Semigroups: Geometry, Measure and an Application
- The interplay between local and non-local master equations: exact and approximated dynamics
- How general are time-local master equations?
- Convex combinations of CP-divisible Pauli channels that are not semigroups
- Singularities, mixing and non-Markovianity of Pauli dynamical maps