Divisibility of quantum dynamical maps and collision models

Abstract

Divisibility of dynamical maps is visualized by trajectories in the parameter space and analyzed within the framework of collision models. We introduce ultimate completely positive (CP) divisible processes, which lose CP divisibility under infinitesimal perturbations, and characterize Pauli dynamical semigroups exhibiting such a property. We construct collision models with factorized environment particles, which realize additivity and multiplicativity of generators of CP divisible maps. A mixture of dynamical maps is obtained with the help of correlated environment. Mixture of ultimate CP divisible processes is shown to result in a new class of eternal CP indivisible evolutions. We explicitly find collision models leading to weakly and essentially non-Markovian Pauli dynamical maps.

Collision models in quantum optics

“…Thereby, the resulting dynamical map will not be CP-divisible. It is signi cant in this respect that CMs with initial correlated bath states can be constructed whose corresponding dynamical map for S reproduces indivisible quantum channels [18,24].…”

“…The last property alongside their simple and intrinsically discrete nature make CMs advantageous case studies to investigate major open problems in quantum non-Markovianity once the basic model outlined above is modi ed so as to introduce a memory mechanism. Among the ways to endow a CM with memory are: adding ancillaancilla collisions [4][5][6][7][8][9][10], embedding S into a larger system [11][12][13][14][15], allowing S to collide with each ancilla more than once [16,17], assuming a correlated initial bath state instead of a product one [18][19][20][21][22][23][24][25] or initial system-bath correlations [26][27][28]. Typical tasks that can be accomplished through NM CMs constructed in one of these ways are: deriving well-de ned (i.e., unconditionally completely positive) NM MEs [4,5,[37][38][39], gaining quantitative information about the role of system-bath and/or intra-bath correlations in making a dynamics NM [6,10,[19][20][21][22], simulating highly NM dynamics or indivisible channels [7,18,24].…”

Decoherence without entanglement and quantum Darwinism

“…A crucial part of our results is the introduction of a new microscopic collisional model [17][18][19][20][21][22][23][24][25] allowing us to compute analytically the dynamics not only of the system but also of the system-environment fragments. Within this framework, we propose a new mechanism, dynamical mixing, that can induce decoherence dynamics on a system without creating any entanglement with its environment.…”

From a posteriori to a priori solutions for a two-level system interacting with a single-photon wavepacket

“…The evolution of a quantum system interacting with the field prepared in the single-photon state is non-Markovian due to the temporal field correlations. The impact of these correlations on the evolution of open systems was analyzed in the framework of the collision model, for instance, in [60,[63][64][65][66]. Discussions about the discrete filtering equations and their continuous limits one can find, for instance, in [54,56,61,67,69,70].…”

“…Discussions about the discrete filtering equations and their continuous limits one can find, for instance, in [54,56,61,67,69,70]. The time discretization procedure leading to the collision model in quantum optics and its connection with the input-output formalism and quantum trajectories are given in [58,60,61].…”