Research

16 pages, 1497 KiB

Open AccessFeature PaperArticle

Geometric Phase of a Transmon in a Dissipative Quantum Circuit

by Ludmila Viotti, Fernando C. Lombardo and Paula I. Villar

Entropy 2024, 26(1), 89; https://doi.org/10.3390/e26010089 - 22 Jan 2024

Viewed by 1248

Superconducting circuits reveal themselves as promising physical devices with multiple uses. Within those uses, the fundamental concept of the geometric phase accumulated by the state of a system shows up recurrently, as, for example, in the construction of geometric gates. Given this framework, [...] Read more.

Superconducting circuits reveal themselves as promising physical devices with multiple uses. Within those uses, the fundamental concept of the geometric phase accumulated by the state of a system shows up recurrently, as, for example, in the construction of geometric gates. Given this framework, we study the geometric phases acquired by a paradigmatic setup: a transmon coupled to a superconductor resonating cavity. We do so both for the case in which the evolution is unitary and when it is subjected to dissipative effects. These models offer a comprehensive quantum description of an anharmonic system interacting with a single mode of the electromagnetic field within a perfect or dissipative cavity, respectively. In the dissipative model, the non-unitary effects arise from dephasing, relaxation, and decay of the transmon coupled to its environment. Our approach enables a comparison of the geometric phases obtained in these models, leading to a thorough understanding of the corrections introduced by the presence of the environment. Full article

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

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22 pages, 3055 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

Viewed by 954

Abstract

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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17 pages, 1284 KiB

Open AccessArticle

Relationship between Information Scrambling and Quantum Darwinism

by Feng Tian, Jian Zou, Hai Li, Liping Han and Bin Shao

Entropy 2024, 26(1), 19; https://doi.org/10.3390/e26010019 - 24 Dec 2023

Viewed by 940

Abstract

A quantum system interacting with a multipartite environment can induce redundant encoding of the information of a system into the environment, which is the essence of quantum Darwinism. At the same time, the environment may scramble the initially localized information about the system. [...] Read more.

A quantum system interacting with a multipartite environment can induce redundant encoding of the information of a system into the environment, which is the essence of quantum Darwinism. At the same time, the environment may scramble the initially localized information about the system. Based on a collision model, we mainly investigate the relationship between information scrambling in an environment and the emergence of quantum Darwinism. Our results show that when the mutual information between the system and environmental fragment is a linear increasing function of the fragment size, the tripartite mutual information (TMI) is zero, which can be proved generally beyond the collision model; when the system exhibits Darwinistic behavior, the TMI is positive (i.e., scrambling does not occur); when we see the behavior of an “encoding” environment, the TMI is negative (i.e., scrambling occurs). Additionally, we give a physical explanation for the above results by considering two simple but illustrative examples. Moreover, depending on the nature of system and environment interactions, it is also shown that the single qubit and two-qubit systems behave differently for the emergence of quantum Darwinism, and hence the scrambling, while their relationship is consistent with the above conclusion. Full article

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

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15 pages, 1607 KiB

Open AccessArticle

Entanglement Degradation in Two Interacting Qubits Coupled to Dephasing Environments

by Rahma Abdelmagid, Khadija Alshehhi and Gehad Sadiek

Entropy 2023, 25(10), 1458; https://doi.org/10.3390/e25101458 - 17 Oct 2023

Viewed by 896

Abstract

One of the main obstacles toward building efficient quantum computing systems is decoherence, where the inevitable interaction between the qubits and the surrounding environment leads to a vanishing entanglement. We consider a system of two interacting asymmetric two-level atoms (qubits) in the presence [...] Read more.

One of the main obstacles toward building efficient quantum computing systems is decoherence, where the inevitable interaction between the qubits and the surrounding environment leads to a vanishing entanglement. We consider a system of two interacting asymmetric two-level atoms (qubits) in the presence of pure and correlated dephasing environments. We study the dynamics of entanglement while varying the interaction strength between the two qubits, their relative frequencies, and their coupling strength to the environment starting from different initial states of practical interest. The impact of the asymmetry of the two qubits, reflected in their different frequencies and coupling strengths to the environment, varies significantly depending on the initial state of the system and its degree of anisotropy. For an initial disentangled, or a Werner, state, as the difference between the frequencies increases, the entanglement decay rate increases, with more persistence at the higher degrees of anisotropy in the former state. However, for an initial anti-correlated Bell state, the entanglement decays more rapidly in the symmetric case compared with the asymmetric one. The difference in the coupling strengths of the two qubits to the pure (uncorrelated) dephasing environment leads to higher entanglement decay in the different initial state cases, though the rate varies depending on the degree of anisotropy and the initial state. Interestingly, the correlated dephasing environment, within a certain range, was found to enhance the entanglement dynamics starting from certain initial states, such as the disentangled, anti-correlated Bell, and Werner, whereas it exhibits a decaying effect in other cases such as the initial correlated Bell state. Full article

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

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14 pages, 754 KiB

Open AccessArticle

A Wigner Quasiprobability Distribution of Work

by Federico Cerisola, Franco Mayo and Augusto J. Roncaglia

Entropy 2023, 25(10), 1439; https://doi.org/10.3390/e25101439 - 11 Oct 2023

Cited by 3 | Viewed by 824

Abstract

In this article, we introduce a quasiprobability distribution of work that is based on the Wigner function. This proposal rests on the idea that the work conducted on an isolated system can be coherently measured by coupling the system to a quantum measurement [...] Read more.

In this article, we introduce a quasiprobability distribution of work that is based on the Wigner function. This proposal rests on the idea that the work conducted on an isolated system can be coherently measured by coupling the system to a quantum measurement apparatus. In this way, a quasiprobability distribution of work can be defined in terms of the Wigner function of the apparatus. This quasidistribution contains the information of the work statistics and also holds a clear operational definition that can be directly measured in a real experiment. Moreover, it is shown that the presence of quantum coherence in the energy eigenbasis is related with the appearance of features related to non-classicality in the Wigner function such as negativity and interference fringes. On the other hand, from this quasiprobability distribution, it is straightforward to obtain the standard two-point measurement probability distribution of work and also the difference in average energy for initial states with coherences. Full article

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

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17 pages, 887 KiB

Open AccessArticle

Emulating Non-Hermitian Dynamics in a Finite Non-Dissipative Quantum System

by Eloi Flament, François Impens and David Guéry-Odelin

Entropy 2023, 25(9), 1256; https://doi.org/10.3390/e25091256 - 24 Aug 2023

Viewed by 1172

Abstract

We discuss the emulation of non-Hermitian dynamics during a given time window using a low-dimensional quantum system coupled to a finite set of equidistant discrete states acting as an effective continuum. We first emulate the decay of an unstable state and map the [...] Read more.

We discuss the emulation of non-Hermitian dynamics during a given time window using a low-dimensional quantum system coupled to a finite set of equidistant discrete states acting as an effective continuum. We first emulate the decay of an unstable state and map the quasi-continuum parameters, enabling the precise approximation of non-Hermitian dynamics. The limitations of this model, including in particular short- and long-time deviations, are extensively discussed. We then consider a driven two-level system and establish criteria for non-Hermitian dynamics emulation with a finite quasi-continuum. We quantitatively analyze the signatures of the finiteness of the effective continuum, addressing the possible emergence of non-Markovian behavior during the time interval considered. Finally, we investigate the emulation of dissipative dynamics using a finite quasi-continuum with a tailored density of states. We show through the example of a two-level system that such a continuum can reproduce non-Hermitian dynamics more efficiently than the usual equidistant quasi-continuum model. Full article

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

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18 pages, 939 KiB

Open AccessFeature PaperArticle

Adiabatic Shortcuts Completion in Quantum Field Theory: Annihilation of Created Particles

by Nicolás F. Del Grosso, Fernando C. Lombardo, Francisco D. Mazzitelli and Paula I. Villar

Entropy 2023, 25(9), 1249; https://doi.org/10.3390/e25091249 - 23 Aug 2023

Viewed by 1375

Abstract

Shortcuts to adiabaticity (STA) are relevant in the context of quantum systems, particularly regarding their control when they are subjected to time-dependent external conditions. In this paper, we investigate the completion of a nonadiabatic evolution into a shortcut to adiabaticity for a quantum [...] Read more.

Shortcuts to adiabaticity (STA) are relevant in the context of quantum systems, particularly regarding their control when they are subjected to time-dependent external conditions. In this paper, we investigate the completion of a nonadiabatic evolution into a shortcut to adiabaticity for a quantum field confined within a one-dimensional cavity containing two movable mirrors. Expanding upon our prior research, we characterize the field’s state using two Moore functions that enables us to apply reverse engineering techniques in constructing the STA. Regardless of the initial evolution, we achieve a smooth extension of the Moore functions that implements the STA. This extension facilitates the computation of the mirrors’ trajectories based on the aforementioned functions. Additionally, we draw attention to the existence of a comparable problem within nonrelativistic quantum mechanics. Full article

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

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14 pages, 541 KiB

Open AccessArticle

Dephasing Dynamics in a Non-Equilibrium Fluctuating Environment

by Xiangjia Meng, Yaxin Sun, Qinglong Wang, Jing Ren, Xiangji Cai and Artur Czerwinski

Entropy 2023, 25(4), 634; https://doi.org/10.3390/e25040634 - 08 Apr 2023

Viewed by 1060

Abstract

We performed a theoretical study of the dephasing dynamics of a quantum two-state system under the influences of a non-equilibrium fluctuating environment. The effect of the environmental non-equilibrium fluctuations on the quantum system is described by a generalized random telegraph noise (RTN) process, [...] Read more.

We performed a theoretical study of the dephasing dynamics of a quantum two-state system under the influences of a non-equilibrium fluctuating environment. The effect of the environmental non-equilibrium fluctuations on the quantum system is described by a generalized random telegraph noise (RTN) process, of which the statistical properties are both non-stationary and non-Markovian. Due to the time-homogeneous property in the master equations for the multi-time probability distribution, the decoherence factor induced by the generalized RTN with a modulatable-type memory kernel can be exactly derived by means of a closed fourth-order differential equation with respect to time. In some special limit cases, the decoherence factor recovers to the expression of the previous ones. We analyzed in detail the environmental effect of memory modulation in the dynamical dephasing in four types of dynamics regimes. The results showed that the dynamical dephasing of the quantum system and the conversion between the Markovian and non-Markovian characters in the dephasing dynamics under the influence of the generalized RTN can be effectively modulated via the environmental memory kernel. Full article

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

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12 pages, 923 KiB

Open AccessArticle

Interplay between Non-Markovianity of Noise and Dynamics in Quantum Systems

by Arzu Kurt

Entropy 2023, 25(3), 501; https://doi.org/10.3390/e25030501 - 14 Mar 2023

Viewed by 1087

Abstract

The non-Markovianity of open quantum system dynamics is often associated with the bidirectional interchange of information between the system and its environment, and it is thought to be a resource for various quantum information tasks. We have investigated the non-Markovianity of the dynamics [...] Read more.

The non-Markovianity of open quantum system dynamics is often associated with the bidirectional interchange of information between the system and its environment, and it is thought to be a resource for various quantum information tasks. We have investigated the non-Markovianity of the dynamics of a two-state system driven by continuous time random walk-type noise, which can be Markovian or non-Markovian depending on its residence time distribution parameters. Exact analytical expressions for the distinguishability as well as the trace distance and entropy-based non-Markovianity measures are obtained and used to investigate the interplay between the non-Markovianity of the noise and that of dynamics. Our results show that, in many cases, the dynamics are also non-Markovian when the noise is non-Markovian. However, it is possible for Markovian noise to cause non-Markovian dynamics and for non-Markovian noise to cause Markovian dynamics but only for certain parameter values. Full article

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

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