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Mathematics
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Theory of Open Quantum Systems and Its Applications
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Theory of Open Quantum Systems and Its Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E4: Mathematical Physics".

Deadline for manuscript submissions: closed (31 January 2024) | Viewed by 4282

Special Issue Editor

Dr. Alexander Teretenkov

E-Mail Website
Guest Editor
Department of Mathematical Methods for Quantum Technologies, Steklov Mathematical Institute of Russian Academy of Sciences, Moscow 119991, Russia
Interests: irreversible quantum evolution; Gorini-Kossakowski-Sudarshan-Lindblad equation; exactly solvable models; non-Markovian evolution

Special Issue Information

Dear Colleagues,

The theory of open quantum systems has been one of the fastest-growing fields in recent decades with an immeasurable number of specific physical applications. Although much has been done, this process has only intensified in recent years. Great progress has been made both in such “classical” open quantum systems topics as Markovian master equations, and in non-Markovian dynamics and the description of multi-time correlation behaviour. Many new applications and mutual enrichment come from the intersection of open quantum systems theory and rapidly evolving areas such as quantum information theory, quantum thermodynamics and quantum control theory. Thus, it is important to initiate this Special Issue dedicated to recent developments in the area. All contributions with novel results related to open quantum systems theory or its applications are welcome.

Dr. Alexander Teretenkov
Guest Editor

Manuscript Submission Information

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Keywords

  • open quantum systems
  • quantum master equations
  • quantum non-Markovianity
  • quantum multi-time correlations
  • decoherence
  • quantum thermodynamics

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Published Papers (3 papers)

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Research

18 pages, 338 KiB  
Article
Long-Term Behaviour in an Exactly Solvable Model of Pure Decoherence and the Problem of Markovian Embedding
by Anton Trushechkin
Mathematics 2024, 12(1), 1; https://doi.org/10.3390/math12010001 - 19 Dec 2023
Cited by 3 | Viewed by 1355
Abstract
We consider a well-known, exactly solvable model of an open quantum system with pure decoherence. The aim of this paper is twofold. Firstly, decoherence is a property of open quantum systems important for both quantum technologies and the fundamental question of the quantum–classical [...] Read more.
We consider a well-known, exactly solvable model of an open quantum system with pure decoherence. The aim of this paper is twofold. Firstly, decoherence is a property of open quantum systems important for both quantum technologies and the fundamental question of the quantum–classical transition. It is worth studying how the long-term rate of decoherence depends on the spectral density characterising the system–bath interaction in this exactly solvable model. Secondly, we address a more general problem of the Markovian embedding of non-Markovian open system dynamics. It is often assumed that a non-Markovian open quantum system can be embedded into a larger Markovian system. However, we show that such embedding is possible only for Ohmic spectral densities (for the case of a positive bath temperature) and is impossible for both sub- and super-Ohmic spectral densities. On the other hand, for Ohmic spectral densities, an asymptotic large-time Markovianity (in terms of the quantum regression formula) takes place. Full article
(This article belongs to the Special Issue Theory of Open Quantum Systems and Its Applications)
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11 pages, 267 KiB  
Article
Assisted Postselective Quantum Transformations and an Improved Photon Number Splitting Attack Strategy
by Timur Klevtsov and Dmitry Kronberg
Mathematics 2023, 11(24), 4973; https://doi.org/10.3390/math11244973 - 16 Dec 2023
Cited by 3 | Viewed by 858
Abstract
Postselective transformations of quantum states is a broader class of operations than deterministic quantum channels. Here, we describe the possibility of increasing the success probability of postselective operations by using additional information, which has a form of pure quantum states and should not [...] Read more.
Postselective transformations of quantum states is a broader class of operations than deterministic quantum channels. Here, we describe the possibility of increasing the success probability of postselective operations by using additional information, which has a form of pure quantum states and should not be changed in case of success. We describe the conditions under which assistance becomes useful, and provide application of our method which improves the efficiency of photon number splitting attack for a variant of SARG04 quantum key distribution protocol. In our attack scenario, one extra photon, which is unchanged, plays the role of assistance. Full article
(This article belongs to the Special Issue Theory of Open Quantum Systems and Its Applications)
19 pages, 383 KiB  
Article
Memory Tensor for Non-Markovian Dynamics with Random Hamiltonian
by Alexander Evgen’evich Teretenkov
Mathematics 2023, 11(18), 3854; https://doi.org/10.3390/math11183854 - 8 Sep 2023
Cited by 2 | Viewed by 1470
Abstract
In the theory of open quantum systems, the Markovian approximation is very widespread. Usually, it assumes the Gorini–Kossakowski–Sudarshan–Lindblad (GKSL) equation for density matrix dynamics and quantum regression formulae for multi-time correlation functions. Nevertheless, now, quantum non-Markovianity is being actively studied, especially the non-Markovianity [...] Read more.
In the theory of open quantum systems, the Markovian approximation is very widespread. Usually, it assumes the Gorini–Kossakowski–Sudarshan–Lindblad (GKSL) equation for density matrix dynamics and quantum regression formulae for multi-time correlation functions. Nevertheless, now, quantum non-Markovianity is being actively studied, especially the non-Markovianity of multi-time correlations. In this work, we consider dynamics with a random Hamiltonian, which can lead to GKSL dynamics of the density matrix for some special cases, but correlation functions generally do not satisfy the quantum regression formulae. Despite the fact that random Hamiltonians have been actively studied, dynamics with such Hamiltonians has been little discussed from the viewpoint of multi-time correlations. For specific models with a random Hamiltonian, we provide the formulae for multi-time correlations which occur instead of the usual regression formulae. Moreover, we introduce and calculate the memory tensor, which characterizes multi-time correlations against the Markovian ones. We think that, despite being applied to specific models, the methods developed in this work can be used in a much broader setup. Full article
(This article belongs to the Special Issue Theory of Open Quantum Systems and Its Applications)
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