scholarly journals Quantum Dynamics in a Fluctuating Environment

Entropy ◽  
2019 ◽  
Vol 21 (11) ◽  
pp. 1040 ◽  
Author(s):  
Xiangji Cai
Keyword(s):  
Quantum Dynamics ◽  
Quantum Information Processing ◽  
Open Quantum Systems ◽  
Master Equations ◽  
Operator Technique ◽  
Dynamical Equations ◽  
Fluctuating Environment ◽  
Qubit System ◽  
Projection Operator Technique ◽  
Tunneling Coupling

We theoretically investigate the dynamics of a quantum system which is coupled to a fluctuating environment based on the framework of Kubo-Anderson spectral diffusion. By employing the projection operator technique, we derive two types of dynamical equations, namely, time-convolution and time-convolutionless quantum master equations, respectively. We derive the exact quantum master equations of a qubit system with both diagonal splitting and tunneling coupling when the environmental noise is subject to a random telegraph process and a Ornstein-Uhlenbeck process, respectively. For the pure decoherence case with no tunneling coupling, the expressions of the decoherence factor we obtained are consistent with the well-known existing ones. The results are significant to quantum information processing and helpful for further understanding the quantum dynamics of open quantum systems.

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 Description of Quantum Dynamics of Open Systems Based on Collision-Like Models

2005 ◽  
Vol 12 (01) ◽  
pp. 81-91 ◽  
Author(s):  
Mário Ziman ◽  
Peter Štelmachovič ◽  
Vladimír Bužek
Keyword(s):  
Quantum System ◽  
Quantum Dynamics ◽  
Open Systems ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Master Equations ◽  
Discrete Dynamics ◽  
Completely Positive ◽  
Semigroup Property ◽  
System A

Master equations in the Lindblad form describe evolution of open quantum systems that are completely positive and simultaneously have a semigroup property. We analyze the possibility to derive this type of master equations from an intrinsically discrete dynamics that is modelled as a sequence of collisions between a given quantum system (a qubit) with particles that form the environment. In order to illustrate our approach we analyze in detail how the process of an exponential decay and the process of decoherence can be derived from a collision-like model in which particular collisions are described by SWAP and controlled-NOT interactions, respectively.

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 Local Information as an Essential Factor for Quantum Entanglement

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 728
Author(s):  
Zhaofeng Su
Keyword(s):  
Quantum Entanglement ◽  
Quantum Information Processing ◽  
Local Information ◽  
Essential Factor ◽  
Qubit System ◽  
Local Vectors ◽  
Correlation Parameters ◽  
The One ◽  
Local Parameters

Quantum entanglement is not only a fundamental concept in quantum mechanics but also a special resource for many important quantum information processing tasks. An intuitive way to understand quantum entanglement is to analyze its geometric parameters which include local parameters and correlation parameters. The correlation parameters have been extensively studied while the role of local parameters have not been drawn attention. In this paper, we investigate the question how local parameters of a two-qubit system affect quantum entanglement in both quantitative and qualitative perspective. Firstly, we find that the concurrence, a measure of quantum entanglement, of a general two-qubit state is bounded by the norms of local vectors and correlations matrix. Then, we derive a sufficient condition for a two-qubit being separable in perspective of local parameters. Finally, we find that different local parameters could make a state with fixed correlation matrix separable, entangled or even more qualitatively entangled than the one with vanished local parameters.

scholarly journals Experimental implementation of precisely tailored light-matter interaction via inverse engineering

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Ying Yan ◽  
Chunyan Shi ◽  
Adam Kinos ◽  
Hafsa Syed ◽  
Sebastian P. Horvath ◽  
...  
Keyword(s):  
Quantum Dynamics ◽  
Quantum Control ◽  
Quantum Information Processing ◽  
Rare Earth Ions ◽  
Adiabatic Process ◽  
Physical Constraints ◽  
Shortcuts To Adiabaticity ◽  
Experimental Implementation ◽  
Speed Up ◽  
Light Matter Interaction

AbstractAccurate and efficient quantum control in the presence of constraints and decoherence is a requirement and a challenge in quantum information processing. Shortcuts to adiabaticity, originally proposed to speed up the slow adiabatic process, have nowadays become versatile toolboxes for preparing states or controlling the quantum dynamics. Unique shortcut designs are required for each quantum system with intrinsic physical constraints, imperfections, and noise. Here, we implement fast and robust control for the state preparation and state engineering in a rare-earth ions system. Specifically, the interacting pulses are inversely engineered and further optimized with respect to inhomogeneities of the ensemble and the unwanted interaction with other qubits. We demonstrate that our protocols surpass the conventional adiabatic schemes, by reducing the decoherence from the excited-state decay and inhomogeneous broadening. The results presented here are applicable to other noisy intermediate-scale quantum systems.

scholarly journals Magnetic Response of Pr1-xLaCexCuO4 in Comparison with Hole-Doped Cuprates

2014 ◽  
Vol 215 ◽  
pp. 11-16
Author(s):  
Alexei Sherman
Keyword(s):  
Magnetic Susceptibility ◽  
Superconducting State ◽  
Projection Operator ◽  
Low Frequency ◽  
Spin Excitation ◽  
Magnetic Response ◽  
Operator Technique ◽  
Electron Band ◽  
Spin Excitations ◽  
Projection Operator Technique

The magnetic susceptibility of the optimally doped Pr1-xLaCexCuO4in the superconducting state is calculated using thet-Jmodel of Cu-O planes, the Mori projection operator technique, and the dispersion of electron bands derived from photoemission experiments. The electron band folding across the antiferromagnetic Brillouin zone border, which is inherent in the crystal, leads to a commensurate low-frequency response. The same band folding causes the appearance of a supplementary spin-excitation branch, which coexists with usual spin excitations. This coexistence can explain two maxima observed in the frequency dependence of the susceptibility. The two nested spin-excitation branches lead to a comb of closely spaced peaks in momentum cuts, which presumably are not resolved in experiment, being seen as a broad commensurate peak up to 100 meV. Reasons for differences in magnetic responses of electron- and hole-doped cuprates are discussed.

scholarly journals Stochastic Master Equations in Thermal Environment

2010 ◽  
Vol 17 (04) ◽  
pp. 389-408 ◽  
Author(s):  
Stéphane Attal ◽  
Clément Pellegrini
Keyword(s):  
Thermal Environment ◽  
Open Quantum Systems ◽  
Heat Bath ◽  
Measurement Model ◽  
Quantum Systems ◽  
Master Equations ◽  
Positive Temperature ◽  
Diffusion Type ◽  
Indirect Measurements ◽  
Pure Diffusion

We derive stochastic master equations which describe the evolution of open quantum systems in contact with a heat bath and undergoing indirect measurements. These equations are obtained as a limit of a quantum repeated measurement model where we consider a small system in contact with an infinite chain at positive temperature. It is well-known that at zero temperature one obtains stochastic differential equations of jump-diffusion type. We show that only pure diffusion type equations are relevant at strictly positive temperatures.

scholarly journals Quantum dephasing induced by non-Markovian random telegraph noise

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Xiangji Cai
Keyword(s):  
Master Equation ◽  
Quantum System ◽  
Conditional Probability ◽  
Quantum Information Processing ◽  
Open Quantum Systems ◽  
Modulation Frequency ◽  
Environmental Noise ◽  
Random Telegraph Noise ◽  
Telegraph Noise ◽  
Generalized Master Equation

AbstractWe theoretically study the dynamical dephasing of a quantum two level system interacting with an environment which exhibits non-Markovian random telegraph fluctuations. The time evolution of the conditional probability of the environmental noise is governed by a generalized master equation depending on the environmental memory effect. The expression of the dephasing factor is derived exactly which is closely associated with the memory kernel in the generalized master equation for the conditional probability of the environmental noise. In terms of three important types memory kernels, we discuss the quantum dephasing dynamics of the system and the non-Markovian character exhibiting in the dynamical dephasing induced by non-Markovian random telegraph noise. We show that the dynamical dephasing of the quantum system does not always exhibit non-Markovian character which results from that the non-Markovian character in the dephasing dynamics depends both on the environmental non-Markovian character and the interaction between the system and environment. In addition, the dynamical dephasing of the quantum system can be modulated by the external modulation frequency of the environment. This result is significant to quantum information processing and helpful for further understanding non-Markovian dynamics of open quantum systems.

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