Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1905.03472 · Open Systems & Information Dynamics

Non-Markovian Open Dynamics from Collision Models

Vijay Pathak, Anil Shaji

Published Dec 1, 2019• 2 citations
arXivHTMLPDF

Abstract

Convex combinations of completely positive (CP) as well as CP-divisible, continuous time dynamical maps arising from collision models are investigated. While the individual maps are both CP and Markovian we find that convex combinations remain CP but not necessarily Markovian. Examples of such combinations for qubit dynamical maps arising from collisional models are worked out and the invertibility, CP-divisibility, P-divisibility as well as Markovian properties of such maps are explored.

DOI
10.1142/s1230161219500185

Related papers

Divisibility of quantum dynamical maps and collision models

Sergey N. Filippov, Jyrki Piilo, Sabrina Maniscalco +1 more

The 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. The mixture of ultimate CP divisible processes is shown to result in a class of eternal CP indivisible evolutions. We explicitly find collision models leading to weakly and essentially non-Markovian Pauli dynamical maps.

arXiv:1708.04994•Physical Review A•Sep 14, 2017•84 citations

Eternal non-Markovianity of qubit maps

Vinayak Jagadish, R. Srikanth

As is well known, unital Pauli maps can be eternally non-CP-divisible. In contrast, here we show that in the case of nonunital maps, eternal non-Markovianity in the nonunital part is ruled out. In the unital case, the eternal non-Markovianity can be obtained by a convex combination of two dephasing semigroups, but not all three of them. We study these results and ramifications arising from them.

arXiv:2501.06846•Physical Review A•Apr 18, 2025•0 citations

Non-Markovian dephasing and depolarizing channels

Shrikant Utagi, R. Srikanth, Subhashish Banerjee

We introduce a method to construct non-Markovian variants of completely positive (CP) dynamical maps, particularly, qubit Pauli channels. We identify non-Markovianity with the breakdown in CP divisibility of the map, i.e., appearance of a not-completely positive intermediate map. In particular, we consider the case of non-Markovian dephasing in detail. The eigenvalues of the Choi matrix of the intermediate map crossover at a point which corresponds to a singularity in the canonical decoherence rate of the corresponding master equation and thus to a momentary noninvertibility of the map. Thereafter, the rate becomes negative, indicating non-Markovianity. We quantify the non-Markovianity by two methods, one based on CP divisibility [Hall et al., Phys. Rev. A 89, 042120 (2014)], which does not require optimization but requires normalization to handle the singularity, and another method, based on distinguishability [Breuer et al. Phys. Rev. Lett. 103, 210401 (2009)], which requires optimization but is insensitive to the singularity.

arXiv:1805.11411•Physical Review A•Sep 26, 2018•55 citations

Collision models for open quantum systems coupled to finite environments

Gyaneswar Bhoi, Anil Shaji

We study a system qubit repeatedly interacting with the same environmental qubit, with a reservoir acting on the environment between collisions via a completely positive, trace-preserving map. We show that complete suppression of system--environment correlations uniquely requires a full environmental reset, recovering a semi group dynamics with a time-independent Gorini--Kossakowski--Sudarshan--Lindblad generator, whereas a partial reset yields a continuous transition between Markovian and non-Markovian regimes governed by a single dimensionless relaxation parameter. For a resonant excitation-exchange interaction, we obtain exact closed-form expressions for the Bloch-vector dynamics for both a generalized depolarizing channel and a generalized amplitude-damping channel acting as the reservoir-induced map. Using the Breuer--Laine--Piilo measure and a Choi-matrix CP-divisibility witness, we identify three distinct dynamical regimes across the parameter space: CP-divisible Markovian dynamics, CP-indivisible but P-divisible dynamics, and non-P-divisible non-Markovian dynamics. The boundaries between these regimes, and the structural differences between uniform and anisotropic environmental relaxation, are characterized numerically.

quant-pharXiv:2606.14163•Jun 15, 2026•0 citations

Non-Markovianity criteria for mixtures of noninvertible Pauli dynamical maps

Katarzyna Siudzińska

Abstract We analyze the connections between the non-Markovianity degree of the most general phase-damping qubit maps and their legitimate mixtures. Using the results for image non-increasing dynamical maps, we formulate the necessary and sufficient conditions for the Pauli maps to satisfy specific divisibility criteria. Next, we examine how the non-Markovianity properties for (in general noninvertible) Pauli dynamical maps influence the properties of their convex combinations. Our results are illustrated with instructive examples. For P-divisible maps, we propose a legitimate time-local generator whose all decoherence rates are temporarily infinite.

arXiv:2104.06489•Journal of Physics A Mathematical and Theoretical•Apr 8, 2022•8 citations

Divisibility and Information Flow Notions of Quantum Markovianity for Noninvertible Dynamical Maps

Dariusz Chruściński, ́Angel Rivas, Erling Størmer

We analyze the relation between completely positive (CP) divisibility and the lack of information backflow for an arbitrary-not necessarily invertible-dynamical map. It is well known that CP divisibility always implies a lack of information backflow. Moreover, these two notions are equivalent for invertible maps. In this Letter, it is shown that for a map which is not invertible the lack of information backflow always implies the existence of a completely positive propagator which, however, needs not be trace preserving. Interestingly, for a wide class of image nonincreasing dynamical maps, this propagator becomes trace preserving as well, and hence, the lack of information backflow implies CP divisibility. This result sheds new light into the structure of the time-local generators giving rise to CP-divisible evolutions. We show that if the map is not invertible then positivity of dissipation/decoherence rates is no longer necessary for CP divisibility.

arXiv:1710.06771•Physical Review Letters•Aug 24, 2018•74 citations
Convex combinations of completely positive (CP) as well as CP-divisible, continuous time dynamical maps arising from collision models are investigated. While the individual maps are both CP and Markovian we find that convex combinations remain CP but not necessarily Markovian. Examples of such combinations for qubit dynamical maps arising from collisional models are worked out and the invertibility, CP-divisibility, P-divisibility as well as Markovian properties of such maps are explored.
The 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. The mixture of ultimate CP divisible processes is shown to result in a class of eternal CP indivisible evolutions. We explicitly find collision models leading to weakly and essentially non-Markovian Pauli dynamical maps.
We introduce a method to construct non-Markovian variants of completely positive (CP) dynamical maps, particularly, qubit Pauli channels. We identify non-Markovianity with the breakdown in CP divisibility of the map, i.e., appearance of a not-completely positive intermediate map. In particular, we consider the case of non-Markovian dephasing in detail. The eigenvalues of the Choi matrix of the intermediate map crossover at a point which corresponds to a singularity in the canonical decoherence rate of the corresponding master equation and thus to a momentary noninvertibility of the map. Thereafter, the rate becomes negative, indicating non-Markovianity. We quantify the non-Markovianity by two methods, one based on CP divisibility [Hall et al., Phys. Rev. A 89, 042120 (2014)], which does not require optimization but requires normalization to handle the singularity, and another method, based on distinguishability [Breuer et al. Phys. Rev. Lett. 103, 210401 (2009)], which requires optimization but is insensitive to the singularity.
We study a system qubit repeatedly interacting with the same environmental qubit, with a reservoir acting on the environment between collisions via a completely positive, trace-preserving map. We show that complete suppression of system--environment correlations uniquely requires a full environmental reset, recovering a semi group dynamics with a time-independent Gorini--Kossakowski--Sudarshan--Lindblad generator, whereas a partial reset yields a continuous transition between Markovian and non-Markovian regimes governed by a single dimensionless relaxation parameter. For a resonant excitation-exchange interaction, we obtain exact closed-form expressions for the Bloch-vector dynamics for both a generalized depolarizing channel and a generalized amplitude-damping channel acting as the reservoir-induced map. Using the Breuer--Laine--Piilo measure and a Choi-matrix CP-divisibility witness, we identify three distinct dynamical regimes across the parameter space: CP-divisible Markovian dynamics, CP-indivisible but P-divisible dynamics, and non-P-divisible non-Markovian dynamics. The boundaries between these regimes, and the structural differences between uniform and anisotropic environmental relaxation, are characterized numerically.
Abstract We analyze the connections between the non-Markovianity degree of the most general phase-damping qubit maps and their legitimate mixtures. Using the results for image non-increasing dynamical maps, we formulate the necessary and sufficient conditions for the Pauli maps to satisfy specific divisibility criteria. Next, we examine how the non-Markovianity properties for (in general noninvertible) Pauli dynamical maps influence the properties of their convex combinations. Our results are illustrated with instructive examples. For P-divisible maps, we propose a legitimate time-local generator whose all decoherence rates are temporarily infinite.
We analyze the relation between completely positive (CP) divisibility and the lack of information backflow for an arbitrary-not necessarily invertible-dynamical map. It is well known that CP divisibility always implies a lack of information backflow. Moreover, these two notions are equivalent for invertible maps. In this Letter, it is shown that for a map which is not invertible the lack of information backflow always implies the existence of a completely positive propagator which, however, needs not be trace preserving. Interestingly, for a wide class of image nonincreasing dynamical maps, this propagator becomes trace preserving as well, and hence, the lack of information backflow implies CP divisibility. This result sheds new light into the structure of the time-local generators giving rise to CP-divisible evolutions. We show that if the map is not invertible then positivity of dissipation/decoherence rates is no longer necessary for CP divisibility.