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

arXiv:0909.0474 · Physical Review A

Redundancy of classical and quantum correlations during decoherence

Juan Pablo Paz, Augusto J. Roncaglia

Published Oct 22, 2009• 61 citations
arXivHTMLPDF

Abstract

We analyze the time dependence of entanglement and total correlations between a system and fractions of its environment in the course of decoherence. For the quantum Brownian motion model, we show that the entanglement and total correlations have rather different dependence on the size of the environmental fraction. Redundancy manifests differently in both types of correlations and can be related with induced classicality. To study this, we present a measure of redundancy and compare it to the existing one.

DOI
10.1103/physreva.80.042111

Related papers

Decoherence and measurement-induced correlations

Shunlong Luo, Nan Li

Decoherence arises from the interaction of a quantum system with the environment or, more precisely, from the measurement in which the environment ``measures'' the quantum system and establishes correlations with it. In this work, we first quantify measurement-induced correlations from both classical and quantum perspectives. Then we quantify decoherence via measurement-induced classical correlations. By virtue of an intrinsic and powerful link between entanglement (as quantified by entanglement of formation) and classical correlations (as quantified by the difference between the total correlations and quantum discord) in pure tripartite systems, we present general analytical formulas for measurement-induced correlations and decoherence measures for qubit systems and, furthermore, reveal a conservation relation for the information-disturbance tradeoff.

Physical Review A•Nov 7, 2011•30 citations

Quantum and Classical Correlations in Quantum Brownian Motion

Jens Eisert, Martin Bodo Plenio

We investigate the entanglement properties of the joint state of a distinguished quantum system and its environment in the quantum Brownian motion model. This model is a frequent starting point for investigations of environment-induced superselection. Using recent methods from quantum information theory, we show that there exists a large class of initial states for which no entanglement will be created at all times between the system of salient interest and the environment. If the distinguished system has been initially prepared in a pure Gaussian state, then entanglement is created immediately, regardless of the temperature of the environment and the nonvanishing coupling.

arXiv:quant-ph/0111016•Physical Review Letters•Sep 5, 2002•76 citations

Redundancy from Subsystem Thermalization

Xiangyu Cao, Zohar Nussinov

In the theory of decoherence, redundancy is the correlation between a quantum system and fractions of the environment. It underlies the emergence of classical behavior. We show that redundancy can persist despite thermalizing dynamics in the environment. This follows an initial broadcasting interaction that changes the density of a conserved quantity. The mutual information between the system and a fraction of the environment is estimated using the large deviation principle governing subsystem thermalization.

quant-pharXiv:2603.15743•Mar 18, 2026•0 citations

Environment-induced two-mode entanglement in quantum Brownian motion

Christian Hörhammer, H. Büttner

The time evolution of quantum correlations of entangled two-mode continuous variable states is examined in single-reservoir as well as two-reservoir models, representing noisy correlated or uncorrelated non-Markovian quantum channels. For this purpose the model of quantum Brownian motion is extended. Various separability criteria for Gaussian continuous variable systems are applied. In both types of reservoir models moderate non-Markovian effects prolong the separability time scales. However, in these models the properties of the stationary state may differ. In the two-reservoir model the initial entanglement is completely lost and both modes are finally uncorrelated. In a common reservoir both modes interact indirectly via the coupling to the same bath variables. Below a critical bath temperature entanglement between the two modes is preserved even in the steady state. A separability criterion is derived, which depends on the bath temperature and the response function of the open quantum system. Thus, the extended quantum Brownian motion model of a two-mode continuous variable system in a common reservoir provides an example of environment-induced entanglement.

arXiv:0708.2670•Physical Review A•Apr 4, 2008•57 citations

Decoherence and the nature of system-environment correlations

A. Pernice, Walter T. Strunz

We investigate system-environment correlations based on the exact dynamics of a qubit and its environment in the framework of pure decoherence (phase damping). We focus on the relation of decoherence and the buildup of system-reservoir entanglement for an arbitrary (possibly mixed) initial qubit state. In the commonly employed regime where the qubit dynamics can be described by a Markov master equation of the Lindblad type, we find that for almost all qubit initial states inside the Bloch sphere, decoherence is complete while the total state is still separable---no entanglement is involved. In general, both ``separable'' and ``entangling'' decoherence occurs, depending on the temperature and initial qubit state. Moreover, we find situations where classical and quantum correlations periodically alternate as a function of time in the regime of low temperatures.

arXiv:1109.0147•Physical Review A•Dec 27, 2011•49 citations

Decoherence

Heinz‐Peter Breuer, Francesco Petruccione

Abstract This chapter deals with the important field of environment-induced decoherence and the transition to the classical behaviour of open quantum systems. A number of techniques is developed that allows the determination of decoherence time scales. The decoherence behaviour in several Markovian models is investigated in detail, such as vacuum and thermal decoherence, decoherence in quantum Brownian motion, and the destruction of coherence through internal degrees of freedom and through the scattering of environmental particles. Moreover, experiments on the decoherence of Schrödinger cat states of the electromagnetic field are discussed, as well as the non-Markovian destruction of quantum coherence in the Caldeira–Leggett model, and the environment-induced selection of a pointer basis in the quantum theory of measurement.

•Jan 25, 2007•8 citations
We analyze the time dependence of entanglement and total correlations between a system and fractions of its environment in the course of decoherence. For the quantum Brownian motion model, we show that the entanglement and total correlations have rather different dependence on the size of the environmental fraction. Redundancy manifests differently in both types of correlations and can be related with induced classicality. To study this, we present a measure of redundancy and compare it to the existing one.
Decoherence arises from the interaction of a quantum system with the environment or, more precisely, from the measurement in which the environment ``measures'' the quantum system and establishes correlations with it. In this work, we first quantify measurement-induced correlations from both classical and quantum perspectives. Then we quantify decoherence via measurement-induced classical correlations. By virtue of an intrinsic and powerful link between entanglement (as quantified by entanglement of formation) and classical correlations (as quantified by the difference between the total correlations and quantum discord) in pure tripartite systems, we present general analytical formulas for measurement-induced correlations and decoherence measures for qubit systems and, furthermore, reveal a conservation relation for the information-disturbance tradeoff.
We investigate the entanglement properties of the joint state of a distinguished quantum system and its environment in the quantum Brownian motion model. This model is a frequent starting point for investigations of environment-induced superselection. Using recent methods from quantum information theory, we show that there exists a large class of initial states for which no entanglement will be created at all times between the system of salient interest and the environment. If the distinguished system has been initially prepared in a pure Gaussian state, then entanglement is created immediately, regardless of the temperature of the environment and the nonvanishing coupling.
In the theory of decoherence, redundancy is the correlation between a quantum system and fractions of the environment. It underlies the emergence of classical behavior. We show that redundancy can persist despite thermalizing dynamics in the environment. This follows an initial broadcasting interaction that changes the density of a conserved quantity. The mutual information between the system and a fraction of the environment is estimated using the large deviation principle governing subsystem thermalization.
The time evolution of quantum correlations of entangled two-mode continuous variable states is examined in single-reservoir as well as two-reservoir models, representing noisy correlated or uncorrelated non-Markovian quantum channels. For this purpose the model of quantum Brownian motion is extended. Various separability criteria for Gaussian continuous variable systems are applied. In both types of reservoir models moderate non-Markovian effects prolong the separability time scales. However, in these models the properties of the stationary state may differ. In the two-reservoir model the initial entanglement is completely lost and both modes are finally uncorrelated. In a common reservoir both modes interact indirectly via the coupling to the same bath variables. Below a critical bath temperature entanglement between the two modes is preserved even in the steady state. A separability criterion is derived, which depends on the bath temperature and the response function of the open quantum system. Thus, the extended quantum Brownian motion model of a two-mode continuous variable system in a common reservoir provides an example of environment-induced entanglement.
We investigate system-environment correlations based on the exact dynamics of a qubit and its environment in the framework of pure decoherence (phase damping). We focus on the relation of decoherence and the buildup of system-reservoir entanglement for an arbitrary (possibly mixed) initial qubit state. In the commonly employed regime where the qubit dynamics can be described by a Markov master equation of the Lindblad type, we find that for almost all qubit initial states inside the Bloch sphere, decoherence is complete while the total state is still separable---no entanglement is involved. In general, both ``separable'' and ``entangling'' decoherence occurs, depending on the temperature and initial qubit state. Moreover, we find situations where classical and quantum correlations periodically alternate as a function of time in the regime of low temperatures.
Abstract This chapter deals with the important field of environment-induced decoherence and the transition to the classical behaviour of open quantum systems. A number of techniques is developed that allows the determination of decoherence time scales. The decoherence behaviour in several Markovian models is investigated in detail, such as vacuum and thermal decoherence, decoherence in quantum Brownian motion, and the destruction of coherence through internal degrees of freedom and through the scattering of environmental particles. Moreover, experiments on the decoherence of Schrödinger cat states of the electromagnetic field are discussed, as well as the non-Markovian destruction of quantum coherence in the Caldeira–Leggett model, and the environment-induced selection of a pointer basis in the quantum theory of measurement.