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This article presents several results establishing connections be- tween Markov chains and dynamical systems, from the point of view of open systems in physics. We show how all Markov chains can be understood as the information on one…

Probability · Mathematics 2010-10-18 Stéphane Attal

A wide class of non-Markovian completely positive master equations can be formulated on the basis of quantum collisional models. In this phenomenological approach the dynamics of an open quantum system is modeled through an ensemble of…

Quantum Physics · Physics 2013-09-26 Adrian A. Budini

Manipulation of a quantum system requires the knowledge of how it evolves. To impose that the dynamics of a system becomes a particular target operation (for any preparation of the system), it may be more useful to have an equation of…

Quantum Physics · Physics 2021-07-28 V. Rezvani , A. T. Rezakhani

Superdense coding is a significant technique widely used in quantum information processing. Indeed, it consists of sending two bits of classical information using a single qubit, leading to faster and more efficient quantum communication.…

Quantum Physics · Physics 2024-08-21 Y. Aiache , S. Al-Kuwari , K. El Anouz , A. El Allati

Master equations describing open quantum dynamics are typically first order differential equations. When such dynamics brings the trajectories in state space of more than one initial state to the same point at finite instants in time, the…

Quantum Physics · Physics 2021-12-03 Abhaya S. Hegde , K. P. Athulya , Vijay Pathak , Jyrki Piilo , Anil Shaji

Effective descriptions accounting for the evolution of quantum systems that are acted on by a bath are desirable. As the number of bath degrees of freedom increases and full quantum simulations turn out computationally prohibitive, simpler…

Quantum Physics · Physics 2014-02-18 A. S. Sanz

A stochastic representation of the dynamics of open quantum systems, suitable for non-perturbative system-reservoir interaction, non-Markovian effects and arbitrarily driven systems is presented. It includes the case of driving on…

Statistical Mechanics · Physics 2016-10-05 Jürgen T. Stockburger

Decoherence is often modeled using Markovian master equations that predict exponential suppression of coherence and are frequently used as effective bounds on quantum behavior in complex environments. Such descriptions, however, correspond…

Quantum Physics · Physics 2026-01-27 Ramandeep Dewan

Non-Markovianity has recently attracted large interest due to significant advances in its characterization and its exploitation for quantum information processing. However, up to now, only non-Markovian regimes featuring environment to…

Accurate models of the dynamics of quantum circuits are essential for optimizing and advancing quantum devices. Since first-principles models of environmental noise and dissipation in real quantum systems are often unavailable, deriving…

Quantum Physics · Physics 2024-12-17 Zakhar Popovych , Kurt Jacobs , Georgios Korpas , Jakub Marecek , Denys I. Bondar

Thermodynamics entails a set of mathematical conditions on quantum Markovian dynamics. In particular, strict energy conservation between the system and environment implies that the dissipative dynamical map commutes with the unitary system…

Quantum Physics · Physics 2021-04-07 Roie Dann , Ronnie Kosloff

Estimation of physical parameters is a must in almost any part of science and technology. The enhancement of the performances in this task, e.g., beating the standard classical shot-noise limit, using available physical resources is a major…

Quantum Physics · Physics 2014-01-29 F. Benatti , S. Alipour , A. T. Rezakhani

We demonstrate a surprising connection between pure steady state entanglement and relaxation timescales in an extremely broad class of Markovian open systems, where two (possibly many-body) systems $A$ and $B$ interact locally with a common…

Quantum Physics · Physics 2024-10-17 Andrew Pocklington , Aashish A. Clerk

During the last ten years, the studies on non-Markovian open system dynamics has become increasingly popular and having contributions from diverse set of research communities. This interest has arisen due to fundamental problematics how to…

Quantum Physics · Physics 2020-01-09 C. -F. Li , G. -C. Guo , J. Piilo

We develop dynamical non-Markovian description of quantum computing in weak coupling limit, in lowest order approximation. We show that long range memory of quantum reservoir produces strong interrelation between structure of noise and…

Quantum Physics · Physics 2009-11-07 Robert Alicki , Michal Horodecki , Pawel Horodecki , Ryszard Horodecki

Quantum evolutions are often non-unitary and in such cases, they are frequently regarded as lossy. Such lossiness, however, does not necessarily persist throughout the evolution, and there can often be intermediate time-spans during which…

Quantum Physics · Physics 2025-12-25 Sutapa Saha , Ujjwal Sen

A general method is discussed to obtain Markovian master equations which describe the interaction with the environment in a microscopic and non-perturbative fashion. It is based on combining time-dependent scattering theory with the concept…

Quantum Physics · Physics 2009-11-13 Klaus Hornberger

Non-Markovian dynamics are typically present in the dynamics of open quantum systems. Despite the rich structure of non-Markovian dynamics, their relevance to quantum information processing (QIP) has been rarely discussed. In this work, we…

Quantum Physics · Physics 2025-12-22 Suguru Endo , Hideaki Hakoshima , Tomohiro Shitara

A hidden Markov process is a well known concept in information theory and is used for a vast range of applications such as speech recognition and error correction. We bridge between two disciplines, experimental physics and advanced…

Mesoscale and Nanoscale Physics · Physics 2015-06-24 Ido Kanter , Aviad Frydman , Asaf Ater

Non-Markovian effects in an open-system dynamics are usually associated to information backflows from the environment to the system. However, the way these backflows manifest and how to detect them is unclear. A natural approach is to study…

Quantum Physics · Physics 2020-07-22 Dario De Santis , Markus Johansson , Bogna Bylicka , Nadja K. Bernardes , Antonio Acín
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