scholarly journals Symmetries and monotones in Markovian quantum dynamics

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 261
Author(s):  
Georgios Styliaris ◽  
Paolo Zanardi
Keyword(s):  
Time Evolution ◽  
Quantum Dynamics ◽  
Riemannian Metrics ◽  
Dynamical Evolution ◽  
Information Geometry ◽  
Quantum Systems ◽  
Conserved Quantities ◽  
Initial State ◽  
Markovian Dynamics ◽  
Special Case

What can one infer about the dynamical evolution of quantum systems just by symmetry considerations? For Markovian dynamics in finite dimensions, we present a simple construction that assigns to each symmetry of the generator a family of scalar functions over quantum states that are monotonic under the time evolution. The aforementioned monotones can be utilized to identify states that are non-reachable from an initial state by the time evolution and include all constraints imposed by conserved quantities, providing a generalization of Noether's theorem for this class of dynamics. As a special case, the generator itself can be considered a symmetry, resulting in non-trivial constraints over the time evolution, even if all conserved quantities trivialize. The construction utilizes tools from quantum information-geometry, mainly the theory of monotone Riemannian metrics. We analyze the prototypical cases of dephasing and Davies generators.

scholarly journals Fermionic duality: General symmetry of open systems with strong dissipation and memory

2021 ◽  
Vol 11 (3) ◽  
Author(s):  
Valentin Bruch ◽  
Konstantin Nestmann ◽  
Jens Schulenborg ◽  
Maarten Wegewijs
Keyword(s):  
Time Evolution ◽  
Quantum Dynamics ◽  
Open Systems ◽  
Broad Class ◽  
Open Quantum Systems ◽  
Causal Structure ◽  
Wide Band ◽  
Quantum Systems ◽  
Strong Interactions ◽  
General Symmetry

We consider the exact time-evolution of a broad class of fermionic open quantum systems with both strong interactions and strong coupling to wide-band reservoirs. We present a nontrivial fermionic duality relation between the evolution of states (Schrödinger) and of observables (Heisenberg). We show how this highly nonintuitive relation can be understood and exploited in analytical calculations within all canonical approaches to quantum dynamics, covering Kraus measurement operators, the Choi-Jamiołkowski state, time-convolution and convolutionless quantum master equations and generalized Lindblad jump operators. We discuss the insights this offers into the divisibility and causal structure of the dynamics and the application to nonperturbative Markov approximations and their initial-slip corrections. Our results underscore that predictions for fermionic models are already fixed by fundamental principles to a much greater extent than previously thought.

scholarly journals An efficient quantum algorithm for the time evolution of parameterized circuits

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 512
Author(s):  
Stefano Barison ◽  
Filippo Vicentini ◽  
Giuseppe Carleo
Keyword(s):  
Variational Principle ◽  
Time Evolution ◽  
Quantum Dynamics ◽  
Quantum Algorithm ◽  
Quantum Systems ◽  
Small Time ◽  
Quantum Circuits ◽  
Time Step ◽  
Optimal Linear ◽  
Global Nature

We introduce a novel hybrid algorithm to simulate the real-time evolution of quantum systems using parameterized quantum circuits. The method, named "projected – Variational Quantum Dynamics" (p-VQD) realizes an iterative, global projection of the exact time evolution onto the parameterized manifold. In the small time-step limit, this is equivalent to the McLachlan's variational principle. Our approach is efficient in the sense that it exhibits an optimal linear scaling with the total number of variational parameters. Furthermore, it is global in the sense that it uses the variational principle to optimize all parameters at once. The global nature of our approach then significantly extends the scope of existing efficient variational methods, that instead typically rely on the iterative optimization of a restricted subset of variational parameters. Through numerical experiments, we also show that our approach is particularly advantageous over existing global optimization algorithms based on the time-dependent variational principle that, due to a demanding quadratic scaling with parameter numbers, are unsuitable for large parameterized quantum circuits.

The Quantum Mechanical Density Operator And Its Time Evolution: Quantum Dynamics Using The Quantum Liouville Equation

2006 ◽  
Author(s):  
Abraham Nitzan
Keyword(s):  
Phase Space ◽  
Probability Density ◽  
Time Evolution ◽  
Liouville Equation ◽  
Density Operator ◽  
Quantum Dynamics ◽  
Quantum Mechanical ◽  
Initial Condition ◽  
Initial State ◽  
Thermal Environments

The starting point of the classical description of motion is the Newton equations that yield a phase space trajectory (rN (t), pN (t)) for a given initial condition (rN (0), pN (0)). Alternatively one may describe classical motion in the framework of the Liouville equation (Section (1.2.2)) that describes the time evolution of the phase space probability density f (rN , pN ; t). For a closed system fully described in terms of a well specified initial condition, the two descriptions are completely equivalent. Probabilistic treatment becomes essential in reduced descriptions that focus on parts of an overall system, as was demonstrated in Sections 5.1–5.3 for equilibrium systems, and in Chapters 7 and 8 that focus on the time evolution of classical systems that interact with their thermal environments. This chapter deals with the analogous quantum mechanical problem. Within the limitations imposed by its nature as expressed, for example, by Heisenbergtype uncertainty principles, the Schrödinger equation is deterministic. Obviously it describes a deterministic evolution of the quantum mechanical wavefunction. The analog of the phase space probability density f (rN , pN ; t) is now the quantum mechanical density operator (often referred to as the “density matrix”), whose time evolution is determined by the quantum Liouville equation. Again, when the system is fully described in terms of a well specified initial wavefunction, the two descriptions are equivalent. The density operator formalism can, however, be carried over to situations where the initial state of the system is not well characterized and/or a reduced description of part of the overall system is desired. Such situations are considered later in this chapter.

scholarly journals On non-Markovian Time Evolution in Open Quantum Systems

2007 ◽  
Vol 14 (03) ◽  
pp. 265-274 ◽  
Author(s):  
Andrzej Kossakowski ◽  
Rolando Rebolledo
Keyword(s):  
Time Evolution ◽  
Open System ◽  
Open Quantum Systems ◽  
Vacuum State ◽  
Quantum Systems ◽  
Initial State ◽  
Completely Positive ◽  
Open Quantum

Non-Markovian reduced dynamics of an open system is investigated. In the case when the initial state of the reservoir is the vacuum state, an approximation is introduced which makes it possible to construct a reduced dynamics which is completely positive.

scholarly journals Quantum Correlation Dynamics in Controlled Two-Coupled-Qubit Systems

Entropy ◽  
2020 ◽  
Vol 22 (7) ◽  
pp. 785 ◽  
Author(s):  
Iulia Ghiu ◽  
Roberto Grimaudo ◽  
Tatiana Mihaescu ◽  
Aurelian Isar ◽  
Antonino Messina
Keyword(s):  
Time Evolution ◽  
Quantum Correlation ◽  
Quantum Dynamics ◽  
Quantum Discord ◽  
Quantum Correlations ◽  
Initial State ◽  
Analytical Treatment ◽  
Werner State ◽  
Driven System ◽  
Physical Reasons

We study and compare the time evolutions of concurrence and quantum discord in a driven system of two interacting qubits prepared in a generic Werner state. The corresponding quantum dynamics is exactly treated and manifests the appearance and disappearance of entanglement. Our analytical treatment transparently unveils the physical reasons for the occurrence of such a phenomenon, relating it to the dynamical invariance of the X structure of the initial state. The quantum correlations which asymptotically emerge in the system are investigated in detail in terms of the time evolution of the fidelity of the initial Werner state.

scholarly journals “What Is Life?”: Open Quantum Systems Approach

2021 ◽  
Author(s):  
Andrei Khrennikov ◽  
Irina Basieva
Keyword(s):  
Steady State ◽  
Quantum Dynamics ◽  
Systems Approach ◽  
Open Quantum Systems ◽  
Quantitative Measure ◽  
Second Law Of Thermodynamics ◽  
Quantum Systems ◽  
Order Structure ◽  
Initial State ◽  
Open Quantum

Abstract Recently the quantum formalism and methodology started to be applied to modeling of information processing in biosystems, mainly to the process of decision making and psychological behavior (but some applications to microbiology and genetics are considered as well). Since a living system is fundamentally open (an isolated biosystem is dead), the theory of open quantum systems is the most powerful tool for life-modeling. In this paper, we turn to the famous Schrödinger book “What is life?” and reformulate his speculations in terms of this theory. Schrödinger pointed toorder preservation as one of the main distinguishing features of biosystems. Entropy is the basic quantitative measure of order. In physical systems, entropy has the tendency to increase (Second Law of Thermodynamics for isolated classical systems and dissipation in open classical and quantum systems). Schrödinger emphasized the ability of biosystems to beat this tendency. We demonstrate that systems processing information in the quantum-like way can preservethe order-structure expressed by the quantum (von Neumann or linear) entropy. We emphasize the role of the special class of quantum dynamics and initial states generating the camel-like graphs for entropy-evolution in the process of interaction with a new environment ℰ: 1) entropy (disorder) increasing in the process of adaptation to the specific features of ℰ; 2) entropy decreasing (order increasing) resulting from adaptation; 3) the restoration of order or even its increase for limiting steady state. In the latter case the steady state entropy can be even lower than the entropy of the initial state.

Dynamics of coherence under Markovian and non-Markovian environments

2017 ◽  
Vol 31 (35) ◽  
pp. 1750329 ◽  
Author(s):  
Zhong-Xiao Wang ◽  
Teng Ma ◽  
Shu-Hao Wang ◽  
Tie-Jun Wang ◽  
Chuan Wang
Keyword(s):  
Density Matrix ◽  
Upper Bound ◽  
Quantum Coherence ◽  
Quantum Discord ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Initial State ◽  
Single Qubit ◽  
Markovian Processes ◽  
Markovian Dynamics

The behavior of quantum coherence is studied under Markovian and non-Markovian dynamics for open quantum systems. For single qubit systems, we show that the coherence depending on the off-diagonal elements of the density matrix is the upper bound of the coherence depending on the relative entropy under both Markovian and non-Markovian processes. For two-qubit systems, in both Markovian and non-Markovian processes, quantum discord and coherence show less sensitivity to the initial state than quantum entanglement. We also find that the quantum discord has similar behaviors with coherence under both Markovian and non-Markovian dynamics.

scholarly journals Majorization and Dynamics of Continuous Distributions

Entropy ◽  
2019 ◽  
Vol 21 (6) ◽  
pp. 590
Author(s):  
Ignacio S. Gomez ◽  
Bruno G. da Costa ◽  
Maike A. F. dos Santos
Keyword(s):  
Time Evolution ◽  
Convex Functions ◽  
Quantum Dynamics ◽  
Stationary States ◽  
Continuous Distributions ◽  
Wide Range ◽  
Mixing Dynamics ◽  
Definition Of ◽  
Fokker Planck Equations ◽  
Special Case

In this work we show how the concept of majorization in continuous distributions can be employed to characterize mixing, diffusive, and quantum dynamics along with the H-Boltzmann theorem. The key point lies in that the definition of majorization allows choosing a wide range of convex functions ϕ for studying a given dynamics. By choosing appropriate convex functions, mixing dynamics, generalized Fokker–Planck equations, and quantum evolutions are characterized as majorized ordered chains along the time evolution, being the stationary states the infimum elements. Moreover, assuming a dynamics satisfying continuous majorization, the H-Boltzmann theorem is obtained as a special case for ϕ ( x ) = x ln x .

Time evolution of chaotic quantum systems

1992 ◽  
Vol 219 (2) ◽  
pp. 364
Keyword(s):  
Time Evolution ◽  
Quantum Systems

scholarly journals Multiparticle quantum plasmonics

Nanophotonics ◽  
2020 ◽  
Vol 9 (6) ◽  
pp. 1243-1269 ◽  
Author(s):  
Chenglong You ◽  
Apurv Chaitanya Nellikka ◽  
Israel De Leon ◽  
Omar S. Magaña-Loaiza
Keyword(s):  
Quantum Dynamics ◽  
Degrees Of Freedom ◽  
Single Photon ◽  
Quantum Systems ◽  
Many Body ◽  
Statistical Fluctuations ◽  
Quantum Plasmonics ◽  
Control Of Quantum Systems ◽  
Multiparticle Systems ◽  
Quantum Photonics

AbstractA single photon can be coupled to collective charge oscillations at the interfaces between metals and dielectrics forming a single surface plasmon. The electromagnetic near-fields induced by single surface plasmons offer new degrees of freedom to perform an exquisite control of complex quantum dynamics. Remarkably, the control of quantum systems represents one of the most significant challenges in the field of quantum photonics. Recently, there has been an enormous interest in using plasmonic systems to control multiphoton dynamics in complex photonic circuits. In this review, we discuss recent advances that unveil novel routes to control multiparticle quantum systems composed of multiple photons and plasmons. We describe important properties that characterize optical multiparticle systems such as their statistical quantum fluctuations and correlations. In this regard, we discuss the role that photon-plasmon interactions play in the manipulation of these fundamental properties for multiparticle systems. We also review recent works that show novel platforms to manipulate many-body light-matter interactions. In this spirit, the foundations that will allow nonexperts to understand new perspectives in multiparticle quantum plasmonics are described. First, we discuss the quantum statistical fluctuations of the electromagnetic field as well as the fundamentals of plasmonics and its quantum properties. This discussion is followed by a brief treatment of the dynamics that characterize complex multiparticle interactions. We apply these ideas to describe quantum interactions in photonic-plasmonic multiparticle quantum systems. We summarize the state-of-the-art in quantum devices that rely on plasmonic interactions. The review is concluded with our perspective on the future applications and challenges in this burgeoning field.

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