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

Reviews in Mathematical Physics

Dynamics of two qubits in common environment

E. N. Bratus’, Leonid Andreevich Pastur

Published Apr 28, 2020• 3 citations
Publisher

Abstract

We consider the entanglement evolution of two qubits embedded into disordered multiconnected environment. We model the environment and its interaction with qubits by large random matrices allowing for a possibility to describe environments of meso- and even nanosize. We obtain general formulas for the time dependent reduced density matrix of the qubits corresponding to several cases of the qubit-environment interaction and initial condition. We then work out an analog of the Born–Markov approximation to find the evolution of the widely used entanglement quantifiers: the concurrence, the negativity and the quantum discord. We show that even in this approximation the time evolution of the reduced density matrix can be non-Markovian, thereby describing certain memory effects due to the backaction of the environment on qubits. In particular, we find the vanishing of the entanglement (Entanglement Sudden Death) at finite moments and its revivals (Entanglement Sudden Birth). Our results, partly known and partly new, can be viewed as a manifestation of the universality of certain properties of decoherent qubit evolution which have been found previously in various versions of bosonic macroscopic environment.

DOI
10.1142/s0129055x20600089

Related papers

On the qubits dynamics in random matrix environment

E. N. Bratus’, Leonid Andreevich Pastur

We consider the entanglement evolution of two qubits embedded into disordered multiconnected environment.We model the environment and its interaction with qubits by large random matrices allowing for a possibility to describe environments of meso-and even nanosize.We obtain general formulas for the time dependent reduced density matrix of the qubits corresponding to several cases of the qubit-environment interaction and initial condition.We then workout an analog of Born-Markov approximation to find the evolution of the widely used entanglement quantifiers: the concurrence, the negativity and the quantum discord.We show that even in this approximation the time evolution of the reduced density matrix can be non-Markovian, thereby describing certain memory effects due to the backaction of the environment on qubits.In particular, we find the vanishing of the entanglement at finite moments and its subsequent revivals (entanglement sudden death and entanglement sudden birth).Our results, partly known and partly new, can be viewed as a manifestation of the universality of certain properties of decoherent qubit evolution which have been found previously in various versions of bosonic macroscopic environment.

Journal of Physics Communications•Dec 19, 2017•8 citations

The Dynamics of Quantum Correlations of Two Qubits in a Common Environment Modeled by Large Random Matrices

E. N. Bratus’, Leonid Andreevich Pastur

This paper is a continuation of our previous paper [8], in which we have studied the dynamics of quantum correlations of two qubits embedded each into its own disordered multiconnected environment. We modeled the environment by random matrices of large size allowing for a possibility to describe meso- and even nanoenvironments. In this paper we also study the dynamics of quantum correlations of two qubits but embedded into a common environment which we also model by random matrices of large size. We obtain the large size limit of the reduced density matrix of two qubits. We then use an analog of the Bogolyubov-van Hove (also known as the Born-Markov) approximation of the theory of open systems and statistical mechanics. The approximation does not imply in general the Markovian evolution in our model but allows for sufficiently detailed analysis both analytical and numerical of the evolution of several widely used quantifiers of quantum correlation, mainly entanglement. We find a number of new patterns of qubits dynamics comparing with the case of independent environments studied in [8] and displaying the role of dynamical (indirect, via the environment) correlations in the enhancing and diversification of qubit evolution. Our results, (announced in [9]), can be viewed as a manifestation of the universality of certain properties of the decoherent qubit evolution which have been found previously in various exact and approximate versions of two-qubit models with macroscopic bosonic environment.

arXiv:2005.05222•May 11, 2020•0 citations

Entanglement evolution for quantum trajectories

Sylvain Vogelsberger, Dominique Spehner

Entanglement is a key resource in quantum information. It can be destroyed or sometimes created by interactions with a reservoir. In recent years, much attention has been devoted to the phenomena of entanglement sudden death and sudden birth, i.e., the sudden disappearance or revival of entanglement at finite times resulting from a coupling of the quantum system to its environment [1, 2, 3]. We investigate the evolution of the entanglement of noninteracting qubits coupled to reservoirs under monitoring of the reservoirs by means of continuous measurements. Because of these measurements, the qubits remain at all times in a pure state, which evolves randomly. To each measurement result (or "realization") corresponds a quantum trajectory in the Hilbert space of the qubits. We show that for two qubits coupled to independent baths subjected to local measurements, the average of the qubits' concurrence over all quantum trajectories is either constant or decays exponentially. The corresponding decay rate depends on the measurement scheme only. This result contrasts with the entanglement sudden death phenomenon exhibited by the qubits' density matrix in the absence of measurements. Our analysis applies to arbitrary quantum jump dynamics (photon counting) as well as to quantum state diffusion (homodyne or heterodyne detections) in the Markov limit. We discuss the best measurement schemes to protect the entanglement of the qubits. We also analyze the case of two qubits coupled to a common bath. Then, the average concurrence can vanish at discrete times and may coincide with the concurrence of the density matrix. The results explained in this article have been presented during the "Fifth International Workshop DICE2010" by the first author and have been the subject of a prior publication [4].

Journal of Physics Conference Series•Jul 8, 2011•0 citations

Disentanglement Dynamics in Nonequilibrium Environments

Mingli Chen, Haonan Chen, Tao Han +1 more

We theoretically study the non-Markovian disentanglement dynamics of a two-qubit system coupled to nonequilibrium environments with nonstationary and non-Markovian random telegraph noise statistical properties. The reduced density matrix of the two-qubit system can be expressed as the Kraus representation in terms of the tensor products of the single qubit Kraus operators. We derive the relation between the entanglement and nonlocality of the two-qubit system which are both closely associated with the decoherence function. We identify the threshold values of the decoherence function to ensure the existences of the concurrence and nonlocal quantum correlations for an arbitrary evolution time when the two-qubit system is initially prepared in the composite Bell states and the Werner states, respectively. It is shown that the environmental nonequilibrium feature can suppress the disentanglement dynamics and reduce the entanglement revivals in non-Markovian dynamics regime. In addition, the environmental nonequilibrium feature can enhance the nonlocality of the two-qubit system. Moreover, the entanglement sudden death and rebirth phenomena and the transition between quantum and classical nonlocalities closely depend on the parameters of the initial states and the environmental parameters in nonequilibrium environments.

Entropy•Sep 21, 2022•9 citations

EFFECTS OF CLASSICAL ENVIRONMENTAL NOISE ON ENTANGLEMENT AND QUANTUM DISCORD DYNAMICS

Claudia Benedetti, Fabrizio Buscemi, Paolo Bordone +1 more

We address the effect of classical noise on the dynamics of quantum correlations, entanglement and quantum discord (QD), of two non-interacting qubits initially prepared in a Bell state. The effect of noise is modeled by randomizing the single-qubit transition amplitudes. We address both static and dynamic environmental noise corresponding to interaction with separate and common baths in either Markovian and non-Markovian regimes. In the Markov regime, a monotone decay of the quantum correlations is found, whereas for non-Markovian noise sudden death and revival phenomena may occur, depending on the characteristics of the noise. Entanglement and QD show the same qualitative behavior for all kind of noises considered. On the other hand, we find that separate and common environments may play opposite roles in preserving quantum correlations, depending on the noise regime considered.

arXiv:1209.4201•International Journal of Quantum Information•Dec 1, 2012•72 citations

Non-Markovian dynamics of quantum discord

F. F. Fanchini, T. Werlang, Carlos Alexandre Brasil +2 more

We evaluate the quantum discord dynamics of two qubits in independent and common non-Markovian environments. We compare the dynamics of entanglement with that of quantum discord. For independent reservoirs the quantum discord vanishes only at discrete instants whereas the entanglement can disappear during a finite time interval. For a common reservoir, quantum discord and entanglement can behave very differently with sudden birth of the former but not of the latter. Furthermore, in this case the quantum discord dynamics presents sudden changes in the derivative of its time evolution which is evidenced by the presence of kinks in its behavior at discrete instants of time.

arXiv:0911.1096•Physical Review A•May 11, 2010•464 citations
We consider the entanglement evolution of two qubits embedded into disordered multiconnected environment. We model the environment and its interaction with qubits by large random matrices allowing for a possibility to describe environments of meso- and even nanosize. We obtain general formulas for the time dependent reduced density matrix of the qubits corresponding to several cases of the qubit-environment interaction and initial condition. We then work out an analog of the Born–Markov approximation to find the evolution of the widely used entanglement quantifiers: the concurrence, the negativity and the quantum discord. We show that even in this approximation the time evolution of the reduced density matrix can be non-Markovian, thereby describing certain memory effects due to the backaction of the environment on qubits. In particular, we find the vanishing of the entanglement (Entanglement Sudden Death) at finite moments and its revivals (Entanglement Sudden Birth). Our results, partly known and partly new, can be viewed as a manifestation of the universality of certain properties of decoherent qubit evolution which have been found previously in various versions of bosonic macroscopic environment.
We consider the entanglement evolution of two qubits embedded into disordered multiconnected environment.We model the environment and its interaction with qubits by large random matrices allowing for a possibility to describe environments of meso-and even nanosize.We obtain general formulas for the time dependent reduced density matrix of the qubits corresponding to several cases of the qubit-environment interaction and initial condition.We then workout an analog of Born-Markov approximation to find the evolution of the widely used entanglement quantifiers: the concurrence, the negativity and the quantum discord.We show that even in this approximation the time evolution of the reduced density matrix can be non-Markovian, thereby describing certain memory effects due to the backaction of the environment on qubits.In particular, we find the vanishing of the entanglement at finite moments and its subsequent revivals (entanglement sudden death and entanglement sudden birth).Our results, partly known and partly new, can be viewed as a manifestation of the universality of certain properties of decoherent qubit evolution which have been found previously in various versions of bosonic macroscopic environment.
This paper is a continuation of our previous paper [8], in which we have studied the dynamics of quantum correlations of two qubits embedded each into its own disordered multiconnected environment. We modeled the environment by random matrices of large size allowing for a possibility to describe meso- and even nanoenvironments. In this paper we also study the dynamics of quantum correlations of two qubits but embedded into a common environment which we also model by random matrices of large size. We obtain the large size limit of the reduced density matrix of two qubits. We then use an analog of the Bogolyubov-van Hove (also known as the Born-Markov) approximation of the theory of open systems and statistical mechanics. The approximation does not imply in general the Markovian evolution in our model but allows for sufficiently detailed analysis both analytical and numerical of the evolution of several widely used quantifiers of quantum correlation, mainly entanglement. We find a number of new patterns of qubits dynamics comparing with the case of independent environments studied in [8] and displaying the role of dynamical (indirect, via the environment) correlations in the enhancing and diversification of qubit evolution. Our results, (announced in [9]), can be viewed as a manifestation of the universality of certain properties of the decoherent qubit evolution which have been found previously in various exact and approximate versions of two-qubit models with macroscopic bosonic environment.
Entanglement is a key resource in quantum information. It can be destroyed or sometimes created by interactions with a reservoir. In recent years, much attention has been devoted to the phenomena of entanglement sudden death and sudden birth, i.e., the sudden disappearance or revival of entanglement at finite times resulting from a coupling of the quantum system to its environment [1, 2, 3]. We investigate the evolution of the entanglement of noninteracting qubits coupled to reservoirs under monitoring of the reservoirs by means of continuous measurements. Because of these measurements, the qubits remain at all times in a pure state, which evolves randomly. To each measurement result (or "realization") corresponds a quantum trajectory in the Hilbert space of the qubits. We show that for two qubits coupled to independent baths subjected to local measurements, the average of the qubits' concurrence over all quantum trajectories is either constant or decays exponentially. The corresponding decay rate depends on the measurement scheme only. This result contrasts with the entanglement sudden death phenomenon exhibited by the qubits' density matrix in the absence of measurements. Our analysis applies to arbitrary quantum jump dynamics (photon counting) as well as to quantum state diffusion (homodyne or heterodyne detections) in the Markov limit. We discuss the best measurement schemes to protect the entanglement of the qubits. We also analyze the case of two qubits coupled to a common bath. Then, the average concurrence can vanish at discrete times and may coincide with the concurrence of the density matrix. The results explained in this article have been presented during the "Fifth International Workshop DICE2010" by the first author and have been the subject of a prior publication [4].
We theoretically study the non-Markovian disentanglement dynamics of a two-qubit system coupled to nonequilibrium environments with nonstationary and non-Markovian random telegraph noise statistical properties. The reduced density matrix of the two-qubit system can be expressed as the Kraus representation in terms of the tensor products of the single qubit Kraus operators. We derive the relation between the entanglement and nonlocality of the two-qubit system which are both closely associated with the decoherence function. We identify the threshold values of the decoherence function to ensure the existences of the concurrence and nonlocal quantum correlations for an arbitrary evolution time when the two-qubit system is initially prepared in the composite Bell states and the Werner states, respectively. It is shown that the environmental nonequilibrium feature can suppress the disentanglement dynamics and reduce the entanglement revivals in non-Markovian dynamics regime. In addition, the environmental nonequilibrium feature can enhance the nonlocality of the two-qubit system. Moreover, the entanglement sudden death and rebirth phenomena and the transition between quantum and classical nonlocalities closely depend on the parameters of the initial states and the environmental parameters in nonequilibrium environments.
We address the effect of classical noise on the dynamics of quantum correlations, entanglement and quantum discord (QD), of two non-interacting qubits initially prepared in a Bell state. The effect of noise is modeled by randomizing the single-qubit transition amplitudes. We address both static and dynamic environmental noise corresponding to interaction with separate and common baths in either Markovian and non-Markovian regimes. In the Markov regime, a monotone decay of the quantum correlations is found, whereas for non-Markovian noise sudden death and revival phenomena may occur, depending on the characteristics of the noise. Entanglement and QD show the same qualitative behavior for all kind of noises considered. On the other hand, we find that separate and common environments may play opposite roles in preserving quantum correlations, depending on the noise regime considered.
We evaluate the quantum discord dynamics of two qubits in independent and common non-Markovian environments. We compare the dynamics of entanglement with that of quantum discord. For independent reservoirs the quantum discord vanishes only at discrete instants whereas the entanglement can disappear during a finite time interval. For a common reservoir, quantum discord and entanglement can behave very differently with sudden birth of the former but not of the latter. Furthermore, in this case the quantum discord dynamics presents sudden changes in the derivative of its time evolution which is evidenced by the presence of kinks in its behavior at discrete instants of time.