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22 pages, 3054 KiB

Open AccessArticle

Control of the von Neumann Entropy for an Open Two-Qubit System Using Coherent and Incoherent Drives

by Oleg V. Morzhin and Alexander N. Pechen

Entropy 2024, 26(1), 36; https://doi.org/10.3390/e26010036 - 29 Dec 2023

Cited by 4 | Viewed by 2568 | Correction

This article is devoted to developing an approach for manipulating the von Neumann entropy

S (ρ (t))

of an open two-qubit system with coherent control and incoherent control inducing time-dependent decoherence rates. The following goals are considered: (a) minimizing [...] Read more.

This article is devoted to developing an approach for manipulating the von Neumann entropy

S (ρ (t))

of an open two-qubit system with coherent control and incoherent control inducing time-dependent decoherence rates. The following goals are considered: (a) minimizing or maximizing the final entropy

S (ρ (T))

; (b) steering

S (ρ (T))

to a given target value; (c) steering

S (ρ (T))

to a target value and satisfying the pointwise state constraint

S (ρ (t)) \leq \bar{S}

for a given

\bar{S}

; (d) keeping

S (ρ (t))

constant at a given time interval. Under the Markovian dynamics determined by a Gorini–Kossakowski–Sudarshan–Lindblad type master equation, which contains coherent and incoherent controls, one- and two-step gradient projection methods and genetic algorithm have been adapted, taking into account the specifics of the objective functionals. The corresponding numerical results are provided and discussed. Full article

(This article belongs to the Special Issue Dynamics of Open Quantum Systems: Quantum Fluctuations, Decoherence and Emergent Phenomena)

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19 pages, 1048 KiB

Open AccessArticle

Spreading of Information on a Network: A Quantum View

by Fabio Bagarello, Francesco Gargano, Matteo Gorgone and Francesco Oliveri

Entropy 2023, 25(10), 1438; https://doi.org/10.3390/e25101438 - 11 Oct 2023

Viewed by 1355

Abstract

This paper concerns the modeling of the spread of information through a complex, multi-layered network, where the information is transferred from an initial transmitter to a final receiver. The mathematical model is deduced within the framework of operatorial methods, according to the formal [...] Read more.

H, ρ

)-induced dynamics and one on the Gorini–Kossakowski–Sudarshan–Lindblad (GKSL) equation. For each method, numerical results are presented. Full article

(This article belongs to the Special Issue Quantum Models of Cognition and Decision-Making II)

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19 pages, 383 KiB

Open AccessArticle

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 1584

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 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)

20 pages, 369 KiB

Open AccessArticle

The Franke–Gorini–Kossakowski–Lindblad–Sudarshan (FGKLS) Equation for Two-Dimensional Systems

by Alexander A. Andrianov, Mikhail V. Ioffe, Ekaterina A. Izotova and Oleg O. Novikov

Symmetry 2022, 14(4), 754; https://doi.org/10.3390/sym14040754 - 6 Apr 2022

Cited by 3 | Viewed by 2035

Abstract

Open quantum systems are, in general, described by a density matrix that is evolving under transformations belonging to a dynamical semigroup. They can obey the Franke–Gorini–Kossakowski–Lindblad–Sudarshan (FGKLS) equation. We exhaustively study the case of a Hilbert space of dimension 2. First, we find final fixed states (called pointers) of an evolution of an open system, and we then obtain a general solution to the FGKLS equation and confirm that it converges to a pointer. After this, we check that the solution has physical meaning, i.e., it is Hermitian, positive and has trace equal to 1, and find a moment of time starting from which the FGKLS equation can be used—the range of applicability of the semigroup symmetry. Next, we study the behavior of a solution for a weak interaction with an environment and make a distinction between interacting and non-interacting cases. Finally, we prove that there cannot exist oscillating solutions to the FGKLS equation, which would resemble the behavior of a closed quantum system. Full article

(This article belongs to the Special Issue Symmetry and Quantum Orders)

68 pages, 3761 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Quantum Foundations of Classical Reversible Computing

by Michael P. Frank and Karpur Shukla

Entropy 2021, 23(6), 701; https://doi.org/10.3390/e23060701 - 1 Jun 2021

Cited by 7 | Viewed by 7909

Abstract

The reversible computation paradigm aims to provide a new foundation for general classical digital computing that is capable of circumventing the thermodynamic limits to the energy efficiency of the conventional, non-reversible digital paradigm. However, to date, the essential rationale for, and analysis of, classical reversible computing (RC) has not yet been expressed in terms that leverage the modern formal methods of non-equilibrium quantum thermodynamics (NEQT). In this paper, we begin developing an NEQT-based foundation for the physics of reversible computing. We use the framework of Gorini-Kossakowski-Sudarshan-Lindblad dynamics (a.k.a. Lindbladians) with multiple asymptotic states, incorporating recent results from resource theory, full counting statistics and stochastic thermodynamics. Important conclusions include that, as expected: (1) Landauer’s Principle indeed sets a strict lower bound on entropy generation in traditional non-reversible architectures for deterministic computing machines when we account for the loss of correlations; and (2) implementations of the alternative reversible computation paradigm can potentially avoid such losses, and thereby circumvent the Landauer limit, potentially allowing the efficiency of future digital computing technologies to continue improving indefinitely. We also outline a research plan for identifying the fundamental minimum energy dissipation of reversible computing machines as a function of speed. Full article

(This article belongs to the Special Issue Physical Information and the Physical Foundations of Computation)

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