Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Chinese Physics

Entropy as a measure of the noise extent in a two-level quantum feedback controlled system

Wang Tao-Bo, Mao-Fa Fang, Yao-Hua Hu

Published Dec 20, 2006• 3 citations
Publisher

Abstract

By introducing the von Neumann entropy as a measure of the extent of noise, this paper discusses the entropy evolution in a two-level quantum feedback controlled system. The results show that the feedback control can induce the reduction of the degree of noise, and different control schemes exhibit different noise controlling ability, the extent of the reduction also related with the position of the target state on the Bloch sphere. It is shown that the evolution of entropy can provide a real time noise observation and a systematic guideline to make reasonable choice of control strategy.

DOI
10.1088/1009-1963/16/1/020

Related papers

Analysis on the von Neumann entropy under the measurement-based feedback control

Kohei Kobayashi

The measurement-based feedback (MBF) control offers several powerful means for preparing the desired target quantum state. Therefore, it is important to investigate fundamental properties of MBF. In particular, how the entropy of the controlled system under the MBF behaves is of great interest. In this study, we examine this problem by deriving a sufficient condition that the time derivative of the von Neumann entropy is nonnegative under the MBF control. This result is rigorously characterized by the variance of the system observable and the quantumness of a given decoherence. We show the validity of the result and physical interpretation in the example of qubit stabilizing.

arXiv:2408.17442•Aug 30, 2024•0 citations

Precise quantum control via unsharp measurements and feedback operations

Du Ran, Ye‐Hong Chen, Zhi‐Cheng Shi +3 more

In this paper, we propose a scheme to eliminate the influence of noises on system dynamics, by means of a sequential unsharp measurements and unitary feedback operations. The unsharp measurements are carried out periodically during system evolution, while the feedback operations are well designed based on the eigenstates of the density matrices of the exact (noiseless) dynamical states and its corresponding post-measurement states. For illustrative examples, we show that the dynamical trajectory errors caused by both static and non-static noises are successfully eliminated in typical two-level and multi-level systems, i.e., the high-fidelity quantum dynamics can be maintained. Furthermore, we discuss the influence of noise strength and measurement strength on the degree of precise quantum control. Crucially, the measurement-feedback scheme is quite universal in that it can be applied to precise quantum control for any dimension systems. Thus, it naturally finds extensive applications in quantum information processing.

arXiv:1809.06725•Sep 18, 2018•0 citations

Exponential stabilization of two-level quantum systems based on continuous noise-assisted feedback

Jie Wen, Yuanhao Shi, Jianfang Jia +1 more

The exponential stabilization of the eigenstates for two-level quantum systems based on continuous noise-assisted feedback control is investigated in this paper. Due to the symmetric structure of state space, quantum systems may converge to an undesired eigenstate under continuous measurement. In order to overcome the convergence obstacle, the continuous noise-assisted feedback strategy, in which the control signal is driven by an exogenous Brownian noise, is proposed to make the quantum systems converge to the target eigenstates exponentially, and the noise gain is designed as a continuously differentiable function of quantum state, which is negatively related to the distance between system state and the target eigenstate. In particular, the exponential convergence is proved based on the stability theory of stochastic differential equations. Moreover, the numerical simulations on a two-level quantum system are performed to verify the effectiveness of noise-assisted feedback control and study the influences of physical parameters and control parameters on convergence rate.

Results in Physics•Feb 21, 2021•15 citations

Decoherence Suppression of Two-level Quantum Systems Based on Coherent Control

Jianyong Li, Jing Zhang

The decoherence suppression issue is studied for two-level quantum systems based on coherent control strategy.The model of two-level open quantum systems under coherent control is formulated,in which the decoherence suppression is equivalent to the decoupling problem of the system from environmental noises.Then,an open-loop control is designed to suppress decoherence,which is shown to be capable of asymptotically decoupling a part of the dynamic variables of the system from the environmental noises.Finally,feedback control strategy is introduced so that the corresponding state variables can be precisely decoupled form the environmental noises without being affected by the noises induced by quantum measurement in feedback control.

Kongzhi yu juece•Jan 1, 2006•1 citation

Quantum control by von Neumann measurements

Alexander Nikolaevich Pechen, N. Il’in, Feng Shuang +1 more

A general scheme is presented for controlling quantum systems using evolution driven by nonselective von Neumann measurements, with or without an additional tailored electromagnetic field. As an example, a two-level quantum system controlled by nonselective quantum measurements is considered. The control goal is to find optimal system observables such that consecutive nonselective measurement of these observables transforms the system from a given initial state into a state which maximizes the expected value of a target operator (the objective). A complete analytical solution is found including explicit expressions for the optimal measured observables and for the maximal objective value given any target operator, any initial system density matrix, and any number of measurements. As an illustration, upper bounds on measurement-induced population transfer between the ground and the excited states for any number of measurements are found. The anti-Zeno effect is recovered in the limit of an infinite number of measurements. In this limit the system becomes completely controllable. The results establish the degree of control attainable by a finite number of measurements.

arXiv:quant-ph/0606187•Physical Review A•Nov 2, 2006•118 citations

Time evolution of the von Neumann entropy in open quantum system

Kohei Kobayashi

Control of open quantum dynamics is of great interest for realizing quantum technologies. Therefore, it is an important task to quantify and characterize the entropy for open quantum systems under decoherence. In this paper, we study the time evolution of the von Neumann entropy for open quantum systems described by the Lindblad master equation. Note that, in particular, when the decoherence corresponds to the measurement for the observable in the system, the von Neumann entropy tends to monotonically increases as the variance becomes larger. Furthermore, we present a lower bound of the von Neumann entropy in the long-time limit. This lower bound has advantages of being straightforwardly calculated and applicable to a general Markovian open quantum system.

arXiv:2405.11824•May 20, 2024•1 citation
By introducing the von Neumann entropy as a measure of the extent of noise, this paper discusses the entropy evolution in a two-level quantum feedback controlled system. The results show that the feedback control can induce the reduction of the degree of noise, and different control schemes exhibit different noise controlling ability, the extent of the reduction also related with the position of the target state on the Bloch sphere. It is shown that the evolution of entropy can provide a real time noise observation and a systematic guideline to make reasonable choice of control strategy.
The measurement-based feedback (MBF) control offers several powerful means for preparing the desired target quantum state. Therefore, it is important to investigate fundamental properties of MBF. In particular, how the entropy of the controlled system under the MBF behaves is of great interest. In this study, we examine this problem by deriving a sufficient condition that the time derivative of the von Neumann entropy is nonnegative under the MBF control. This result is rigorously characterized by the variance of the system observable and the quantumness of a given decoherence. We show the validity of the result and physical interpretation in the example of qubit stabilizing.
In this paper, we propose a scheme to eliminate the influence of noises on system dynamics, by means of a sequential unsharp measurements and unitary feedback operations. The unsharp measurements are carried out periodically during system evolution, while the feedback operations are well designed based on the eigenstates of the density matrices of the exact (noiseless) dynamical states and its corresponding post-measurement states. For illustrative examples, we show that the dynamical trajectory errors caused by both static and non-static noises are successfully eliminated in typical two-level and multi-level systems, i.e., the high-fidelity quantum dynamics can be maintained. Furthermore, we discuss the influence of noise strength and measurement strength on the degree of precise quantum control. Crucially, the measurement-feedback scheme is quite universal in that it can be applied to precise quantum control for any dimension systems. Thus, it naturally finds extensive applications in quantum information processing.
The exponential stabilization of the eigenstates for two-level quantum systems based on continuous noise-assisted feedback control is investigated in this paper. Due to the symmetric structure of state space, quantum systems may converge to an undesired eigenstate under continuous measurement. In order to overcome the convergence obstacle, the continuous noise-assisted feedback strategy, in which the control signal is driven by an exogenous Brownian noise, is proposed to make the quantum systems converge to the target eigenstates exponentially, and the noise gain is designed as a continuously differentiable function of quantum state, which is negatively related to the distance between system state and the target eigenstate. In particular, the exponential convergence is proved based on the stability theory of stochastic differential equations. Moreover, the numerical simulations on a two-level quantum system are performed to verify the effectiveness of noise-assisted feedback control and study the influences of physical parameters and control parameters on convergence rate.
The decoherence suppression issue is studied for two-level quantum systems based on coherent control strategy.The model of two-level open quantum systems under coherent control is formulated,in which the decoherence suppression is equivalent to the decoupling problem of the system from environmental noises.Then,an open-loop control is designed to suppress decoherence,which is shown to be capable of asymptotically decoupling a part of the dynamic variables of the system from the environmental noises.Finally,feedback control strategy is introduced so that the corresponding state variables can be precisely decoupled form the environmental noises without being affected by the noises induced by quantum measurement in feedback control.
A general scheme is presented for controlling quantum systems using evolution driven by nonselective von Neumann measurements, with or without an additional tailored electromagnetic field. As an example, a two-level quantum system controlled by nonselective quantum measurements is considered. The control goal is to find optimal system observables such that consecutive nonselective measurement of these observables transforms the system from a given initial state into a state which maximizes the expected value of a target operator (the objective). A complete analytical solution is found including explicit expressions for the optimal measured observables and for the maximal objective value given any target operator, any initial system density matrix, and any number of measurements. As an illustration, upper bounds on measurement-induced population transfer between the ground and the excited states for any number of measurements are found. The anti-Zeno effect is recovered in the limit of an infinite number of measurements. In this limit the system becomes completely controllable. The results establish the degree of control attainable by a finite number of measurements.
Control of open quantum dynamics is of great interest for realizing quantum technologies. Therefore, it is an important task to quantify and characterize the entropy for open quantum systems under decoherence. In this paper, we study the time evolution of the von Neumann entropy for open quantum systems described by the Lindblad master equation. Note that, in particular, when the decoherence corresponds to the measurement for the observable in the system, the von Neumann entropy tends to monotonically increases as the variance becomes larger. Furthermore, we present a lower bound of the von Neumann entropy in the long-time limit. This lower bound has advantages of being straightforwardly calculated and applicable to a general Markovian open quantum system.