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:1504.00671 · Physical Review Letters

Non-Markovianity of Gaussian Channels

Gianpaolo Torre, Wojciech Roga, Fabrizio Illuminati

Published Aug 13, 2015• 38 citations
arXivHTMLPDF

Abstract

We introduce a necessary and sufficient criterion for the non-Markovianity of Gaussian quantum dynamical maps based on the violation of divisibility. The criterion is derived by defining a general vectorial representation of the covariance matrix which is then exploited to determine the condition for the complete positivity of partial maps associated with arbitrary time intervals. Such construction does not rely on the Choi-Jamiolkowski representation and does not require optimization over states.

DOI
10.1103/physrevlett.115.070401

Related papers

Exact non-Markovian dynamics of Gaussian quantum channels: Finite-time and asymptotic regimes

Gianpaolo Torre, Fabrizio Illuminati

We investigate the Markovian and non-Markovian dynamics of Gaussian quantum channels, exploiting a recently introduced necessary and sufficient criterion and the ensuing measure of non-Markovianity based on the violation of the divisibility property of the dynamical map. We compare the paradigmatic instances of quantum Brownian motion (QBM) and pure damping channels, and for the former we find that the exact dynamical evolution is always non-Markovian in the finite-time as well as in the asymptotic regimes for any nonvanishing value of the non-Markovianity parameter. If one resorts to the rotating-wave approximated form of the QBM, that neglects the anomalous diffusion contribution to the system dynamics, we show that such an approximation fails to detect the non-Markovian nature of the dynamics. Finally, for the exact dynamics of the QBM in the asymptotic regime, we show that the quantifiers of non-Markovianity based on the distinguishability between quantum states fail to detect the non-Markovian nature of the dynamics.

arXiv:1804.03095•Physical Review A•Jul 19, 2018•13 citations

Map-Dependent Quantum Characteristic Functions and CP-Divisibility in Non-Markovian Quantum Dynamics

Koichi Nakagawa

We introduce map-dependent quantum characteristic functions constructed from the normalized Choi operator of quantum dynamical maps. We prove a Bochner--Choi positivity theorem establishing that the positive-type condition of the associated Gram matrix is equivalent to complete positivity of the underlying quantum channel. Applying the construction to intermediate dynamical maps, we obtain a characterization of CP-divisibility in terms of positivity of two-time characteristic functions. Numerical examples for amplitude damping and pure dephasing models demonstrate that negativity of the Gram matrix coincides with the breakdown of CP-divisibility and the emergence of information backflow. The proposed framework provides a new bridge between characteristic-function methods in quantum statistics and structural properties of quantum dynamical maps.

quant-pharXiv:2604.17185•Apr 21, 2026•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

Non-Markovian quantum dynamics from symmetric measurements

Katarzyna Siudzińska

We use symmetric measurement operators to construct quantum channels that provide a further generalization of generalized Pauli channels. The resulting maps are bistochastic but, in general, no longer mixed unitary. We analyze their important properties, such as complete positivity and the ability to break quantum entanglement. In the main part, we consider the corresponding open quantum systems dynamics with time-local generators. From the divisibility properties of dynamical maps, we derive sufficient Markovianity and non-Markovianity conditions. As instructive examples, we present the generators of P-divisible generalized Pauli dynamical maps that allow for more negativity in the decoherence rates.

arXiv:2402.04415•Physical Review A•Jul 15, 2024•5 citations

Non-Markovianity criteria for mixtures of noninvertible generalized Pauli dynamical maps

Katarzyna Siudzińska

We analyze the divisibility properties of generalized Pauli dynamical maps. Using the results for image non-increasing dynamical maps, we formulate the conditions for the underlying evolution to satisfy specific non-Markovianity criteria. For the qubit evolution, we find the necessary and sufficient conditions for P and CP-divisibility of the associated, in general noninvertible, Pauli dynamical maps. Finally, we analyze the divisibility degree for mixtures of noninvertible phase-damping channels. For P-divisible maps, we propose a legitimate time-local generator with all temporarily infinite decoherence rates.

•Apr 13, 2021•0 citations

Assessing non-Markovian dynamics through moments of the Choi state

Bivas Mallick, Saheli Mukherjee, Ananda G. Maity +1 more

Non-Markovian effects in open quantum system dynamics usually manifest the backflow of information from the environment to the system, indicating complete-positive divisibility breaking of the dynamics. We provide a criterion for witnessing such non-Markovian dynamics exhibiting information backflow, based on partial moments of Choi matrices. The moment condition determined by the positive semi-definiteness of a matrix does not hold for a Choi state describing non-Markovian dynamics. We then present some explicit examples in support of our proposed non-Markovianity detection scheme. Finally, a moment-based measure of non-Markovianity for unital dynamics is formulated.

arXiv:2303.03615•Physical Review A•Feb 29, 2024•12 citations
We introduce a necessary and sufficient criterion for the non-Markovianity of Gaussian quantum dynamical maps based on the violation of divisibility. The criterion is derived by defining a general vectorial representation of the covariance matrix which is then exploited to determine the condition for the complete positivity of partial maps associated with arbitrary time intervals. Such construction does not rely on the Choi-Jamiolkowski representation and does not require optimization over states.
We investigate the Markovian and non-Markovian dynamics of Gaussian quantum channels, exploiting a recently introduced necessary and sufficient criterion and the ensuing measure of non-Markovianity based on the violation of the divisibility property of the dynamical map. We compare the paradigmatic instances of quantum Brownian motion (QBM) and pure damping channels, and for the former we find that the exact dynamical evolution is always non-Markovian in the finite-time as well as in the asymptotic regimes for any nonvanishing value of the non-Markovianity parameter. If one resorts to the rotating-wave approximated form of the QBM, that neglects the anomalous diffusion contribution to the system dynamics, we show that such an approximation fails to detect the non-Markovian nature of the dynamics. Finally, for the exact dynamics of the QBM in the asymptotic regime, we show that the quantifiers of non-Markovianity based on the distinguishability between quantum states fail to detect the non-Markovian nature of the dynamics.
We introduce map-dependent quantum characteristic functions constructed from the normalized Choi operator of quantum dynamical maps. We prove a Bochner--Choi positivity theorem establishing that the positive-type condition of the associated Gram matrix is equivalent to complete positivity of the underlying quantum channel. Applying the construction to intermediate dynamical maps, we obtain a characterization of CP-divisibility in terms of positivity of two-time characteristic functions. Numerical examples for amplitude damping and pure dephasing models demonstrate that negativity of the Gram matrix coincides with the breakdown of CP-divisibility and the emergence of information backflow. The proposed framework provides a new bridge between characteristic-function methods in quantum statistics and structural properties of quantum 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 use symmetric measurement operators to construct quantum channels that provide a further generalization of generalized Pauli channels. The resulting maps are bistochastic but, in general, no longer mixed unitary. We analyze their important properties, such as complete positivity and the ability to break quantum entanglement. In the main part, we consider the corresponding open quantum systems dynamics with time-local generators. From the divisibility properties of dynamical maps, we derive sufficient Markovianity and non-Markovianity conditions. As instructive examples, we present the generators of P-divisible generalized Pauli dynamical maps that allow for more negativity in the decoherence rates.
We analyze the divisibility properties of generalized Pauli dynamical maps. Using the results for image non-increasing dynamical maps, we formulate the conditions for the underlying evolution to satisfy specific non-Markovianity criteria. For the qubit evolution, we find the necessary and sufficient conditions for P and CP-divisibility of the associated, in general noninvertible, Pauli dynamical maps. Finally, we analyze the divisibility degree for mixtures of noninvertible phase-damping channels. For P-divisible maps, we propose a legitimate time-local generator with all temporarily infinite decoherence rates.
Non-Markovian effects in open quantum system dynamics usually manifest the backflow of information from the environment to the system, indicating complete-positive divisibility breaking of the dynamics. We provide a criterion for witnessing such non-Markovian dynamics exhibiting information backflow, based on partial moments of Choi matrices. The moment condition determined by the positive semi-definiteness of a matrix does not hold for a Choi state describing non-Markovian dynamics. We then present some explicit examples in support of our proposed non-Markovianity detection scheme. Finally, a moment-based measure of non-Markovianity for unital dynamics is formulated.