scholarly journals Memory Effects in Quantum Dynamics Modelled by Quantum Renewal Processes

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 905
Author(s):  
Nina Megier ◽  
Manuel Ponzi ◽  
Andrea Smirne ◽  
Bassano Vacchini
Keyword(s):  
Quantum Dynamics ◽  
Open Quantum System ◽  
Open Quantum Systems ◽  
Phenomenological Approach ◽  
Quantum Systems ◽  
Renewal Processes ◽  
Continuous Part ◽  
Trace Distance ◽  
Open Quantum ◽  
And Control

Simple, controllable models play an important role in learning how to manipulate and control quantum resources. We focus here on quantum non-Markovianity and model the evolution of open quantum systems by quantum renewal processes. This class of quantum dynamics provides us with a phenomenological approach to characterise dynamics with a variety of non-Markovian behaviours, here described in terms of the trace distance between two reduced states. By adopting a trajectory picture for the open quantum system evolution, we analyse how non-Markovianity is influenced by the constituents defining the quantum renewal process, namely the time-continuous part of the dynamics, the type of jumps and the waiting time distributions. We focus not only on the mere value of the non-Markovianity measure, but also on how different features of the trace distance evolution are altered, including times and number of revivals.

scholarly journals Advances in Sequential Measurement and Control of Open Quantum Systems

Proceedings ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 11 ◽  
Author(s):  
Stefano Gherardini ◽  
Andrea Smirne ◽  
Matthias M. Müller ◽  
Filippo Caruso
Keyword(s):  
Quantum System ◽  
Quantum Dynamics ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Noise Sources ◽  
Open Quantum ◽  
Quantum Science ◽  
And Control ◽  
Measurement And Control ◽  
Sequential Measurements

Novel concepts, perspectives and challenges in measuring and controlling an open quantum system via sequential schemes are shown. We discuss how similar protocols, relying both on repeated quantum measurements and dynamical decoupling control pulses, can allow to: (i) Confine and protect quantum dynamics from decoherence in accordance with the Zeno physics. (ii) Analytically predict the probability that a quantum system is transferred into a target quantum state by means of stochastic sequential measurements. (iii) Optimally reconstruct the spectral density of environmental noise sources by orthogonalizing in the frequency domain the filter functions driving the designed quantum-sensor. The achievement of these tasks will enhance our capability to observe and manipulate open quantum systems, thus bringing advances to quantum science and technologies.

Thermodynamics and Control of Open Quantum Systems

2021 ◽  
Author(s):  
Gershon Kurizki ◽  
Abraham G. Kofman
Keyword(s):  
Quantum Chemistry ◽  
Quantum Physics ◽  
Open Quantum Systems ◽  
Condensed Matter ◽  
Quantum Systems ◽  
Open Quantum ◽  
Heat Engines ◽  
Chemistry Research ◽  
And Control ◽  
Quantum Thermodynamic

The control of open quantum systems and their associated quantum thermodynamic properties is a topic of growing importance in modern quantum physics and quantum chemistry research. This unique and self-contained book presents a unifying perspective of such open quantum systems, first describing the fundamental theory behind these formidably complex systems, before introducing the models and techniques that are employed to control their quantum thermodynamics processes. A detailed discussion of real quantum devices is also covered, including quantum heat engines and quantum refrigerators. The theory of open quantum systems is developed pedagogically, from first principles, and the book is accessible to graduate students and researchers working in atomic physics, quantum information, condensed matter physics, and quantum chemistry.

Lyapunov control on quantum systems

2014 ◽  
Vol 28 (30) ◽  
pp. 1430020 ◽  
Author(s):  
L. C. Wang ◽  
X. X. Yi
Keyword(s):  
Quantum System ◽  
Open Quantum System ◽  
Open Quantum Systems ◽  
Logic Gates ◽  
Quantum Systems ◽  
Open Quantum ◽  
Quantum Operations ◽  
Lyapunov Control ◽  
Decoherence Free Subspace ◽  
General Method

We review the scheme of quantum Lyapunov control and its applications into quantum systems. After a brief review on the general method of quantum Lyapunov control in closed and open quantum systems, we apply it into controlling quantum states and quantum operations. The control of a spin-1/2 quantum system, driving an open quantum system into its decoherence free subspace (DFS), constructing single qubit and two-qubit logic gates are taken to illustrate the scheme. The optimalization of the Lyapunov control is also reviewed in this article.

scholarly journals Reduced Operator Approximation for Modelling Open Quantum Systems

2015 ◽  
Vol 22 (02) ◽  
pp. 1550008
Author(s):  
A. Werpachowska
Keyword(s):  
Quantum Dynamics ◽  
Quantum Coherence ◽  
Degrees Of Freedom ◽  
Open Quantum Systems ◽  
Interaction Strength ◽  
Quantum Systems ◽  
Computationally Efficient ◽  
Memory Length ◽  
Open Quantum ◽  
Operator Approximation

We present the reduced operator approximation: a simple, physically transparent and computationally efficient method of modelling open quantum systems. It employs the Heisenberg picture of the quantum dynamics, which allows us to focus on the system degrees of freedom in a natural and easy way. We describe different variants of the method, low- and high-order in the system–bath interaction operators, defining them for either general quantum harmonic oscillator baths or specialising them for independent baths with Lorentzian spectral densities. Its wide applicability is demonstrated on the examples of systems coupled to different baths (with varying system–bath interaction strength and bath memory length), and compared with the exact pseudomode and the popular quantum state diffusion approach. The method captures the decoherence of the system interacting with the bath, while conserving the total energy. Our results suggest that quantum coherence effects persist in open quantum systems for much longer times than previously thought.

scholarly journals On Time-Local Generators of Quantum Evolution

2014 ◽  
Vol 21 (01n02) ◽  
pp. 1440004 ◽  
Author(s):  
Dariusz Chruściński
Keyword(s):  
Quantum Dynamics ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Master Equations ◽  
Quantum Evolution ◽  
Completely Positive ◽  
Open Quantum ◽  
The Family

We present a basic introduction to the dynamics of open quantum systems based on local-in-time master equations. We characterize the properties of time-local generators giving rise to legitimate completely positive trace preserving quantum evolutions. The analysis of Markovian and non-Markovian quantum dynamics is presented as well. The whole discussion is illustrated by the family of many instructive examples.

scholarly journals Hilbert–Schmidt speed as an efficient figure of merit for quantum estimation of phase encoded into the initial state of open n-qubit systems

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Hossein Rangani Jahromi ◽  
Rosario Lo Franco
Keyword(s):  
Figure Of Merit ◽  
Open Quantum System ◽  
Open Quantum Systems ◽  
Quantum Fisher Information ◽  
Quantum Systems ◽  
Phase Estimation ◽  
System State ◽  
Initial State ◽  
Open Quantum ◽  
Derivatives Of

AbstractHilbert–Schmidt speed (HSS) is a special type of quantum statistical speed which is easily computable, since it does not require diagonalization of the system state. We find that, when both HSS and quantum Fisher information (QFI) are calculated with respect to the phase parameter encoded into the initial state of an n-qubit register, the zeros of the HSS dynamics are actually equal to those of the QFI dynamics. Moreover, the signs of the time-derivatives of both HSS and QFI exactly coincide. These findings, obtained via a thorough investigation of several paradigmatic open quantum systems, show that HSS and QFI exhibit the same qualitative time evolution. Therefore, HSS reveals itself as a powerful figure of merit for enhancing quantum phase estimation in an open quantum system made of n qubits. Our results also provide strong evidence for both contractivity of the HSS under memoryless dynamics and its sensitivity to system-environment information backflows to detect the non-Markovianity in high-dimensional systems, as suggested in previous studies.

scholarly journals Quantum Maps with Memory from Generalized Lindblad Equation

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 544
Author(s):  
Vasily E. Tarasov
Keyword(s):  
Discrete Time ◽  
Power Law ◽  
Quantum Dynamics ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Periodic Sequence ◽  
Lindblad Equation ◽  
Open Quantum ◽  
Systems With Memory ◽  
With Memory

In this paper, we proposed the exactly solvable model of non-Markovian dynamics of open quantum systems. This model describes open quantum systems with memory and periodic sequence of kicks by environment. To describe these systems, the Lindblad equation for quantum observable is generalized by taking into account power-law fading memory. Dynamics of open quantum systems with power-law memory are considered. The proposed generalized Lindblad equations describe non-Markovian quantum dynamics. The quantum dynamics with power-law memory are described by using integrations and differentiation of non-integer orders, as well as fractional calculus. An example of a quantum oscillator with linear friction and power-law memory is considered. In this paper, discrete-time quantum maps with memory, which are derived from generalized Lindblad equations without any approximations, are suggested. These maps exactly correspond to the generalized Lindblad equations, which are fractional differential equations with the Caputo derivatives of non-integer orders and periodic sequence of kicks that are represented by the Dirac delta-functions. The solution of these equations for coordinates and momenta are derived. The solutions of the generalized Lindblad equations for coordinate and momentum operators are obtained for open quantum systems with memory and kicks. Using these solutions, linear and nonlinear quantum discrete-time maps are derived.

scholarly journals Preparation of Quantum Gates for Open Quantum Systems by Lyapunov Control Method

2016 ◽  
Vol 23 (01) ◽  
pp. 1650005 ◽  
Author(s):  
Jie Wen ◽  
Shuang Cong
Keyword(s):  
Lyapunov Function ◽  
Control Method ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Quantum Gates ◽  
Control Laws ◽  
Open Quantum ◽  
Matrix Logarithm ◽  
The Matrix ◽  
And Control

In this paper the control laws of preparing quantum gates are designed based on Lyapunov stability theorem for two level open quantum systems. We propose a novel Lyapunov function according to the matrix logarithm function, which has higher accuracy and faster convergence speed by comparing them with those of the Lyapunov function of distance. Based on the proposed function, we design two types of control laws to prepare quantum gates for different systems including Markovian quantum systems with phase damping and amplitude damping, non-Markovian quantum systems and closed quantum systems. Furthermore, the system robustness when the Hamiltonian contains uncertainty is further investigated. In order to verify the superiorities of proposed function and control method, NOT gates are prepared by the designed control laws for different systems in the numerical experiments, and the results are comparatively analyzed.

scholarly journals OPEN QUANTUM DYNAMICS: COMPLETE POSITIVITY AND ENTANGLEMENT

2005 ◽  
Vol 19 (19) ◽  
pp. 3063-3139 ◽  
Author(s):  
FABIO BENATTI ◽  
ROBERTO FLOREANINI
Keyword(s):  
Quantum Entanglement ◽  
Quantum Dynamics ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Complete Positivity ◽  
Information Communication ◽  
Open Quantum ◽  
Statistical Correlations ◽  
Quantum Open System ◽  
Algebraic Constraint

We review the standard treatment of open quantum systems in relation to quantum entanglement, analyzing, in particular, the behavior of bipartite systems immersed in the same environment. We first focus upon the notion of complete positivity, a physically motivated algebraic constraint on the quantum dynamics, in relation to quantum entanglement, i.e. the existence of statistical correlations which can not be accounted for by classical probability. We then study the entanglement power of heat baths versus their decohering properties, a topic of increasing importance in the framework of the fast developing fields of quantum information, communication and computation. The presentation is self contained and, through several examples, it offers a detailed survey of the physics and of the most relevant and used techniques relative to both quantum open system dynamics and quantum entanglement.

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