Quantum-Dynamical Semigroups and the Church of the Larger Hilbert Space
arXiv:2211.08351 · doi:10.1142/S1230161223500038
Abstract
In this work we investigate Stinespring dilations of quantum-dynamical semigroups, which are known to exist by means of a constructive proof given by Davies in the early 70s. We show that if the semigroup describes an open system, that is, if it does not consist of only unitary channels, then the evolution of the dilated closed system has to be generated by an unbounded Hamiltonian; subsequently the environment has to correspond to an infinite-dimensional Hilbert space, regardless of the original system. Moreover, we prove that the second derivative of Stinespring dilations with a bounded total Hamiltonian yields the dissipative part of some quantum-dynamical semigroup -- and vice versa. In particular this characterizes the generators of quantum-dynamical semigroups via Stinespring dilations.
9+9 pages
References in corpus (8)
- Quantum Non-Markovianity: Characterization, Quantification and Detection
- Assessing non-Markovian dynamics
- On measures of non-Markovianity: divisibility vs. backflow of information
- Nonexponential quantum decay under environmental decoherence
- Non-Markovian thermal operations boosting the performance of quantum heat engines
- Capacity of non-Markovianity to boost the efficiency of molecular switches
- Continuous thermomajorization and a complete set of laws for Markovian thermal processes
- Which Bath-Hamiltonians Matter for Thermal Operations?