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:quant-ph/0607219 · Laser Physics

Slipped nonpositive reduced dynamics and entanglement

Fabio Benatti, Roberto Floreanini B, Sébastien Breteaux

Published Sep 28, 2006• 12 citations
arXivHTMLPDF

Abstract

Nonpositive Markov approximations are sometimes used to describe the dynamics of qubits in weak interaction with suitable environments; the appearance of negative probabilities is avoided by assuming that the transient regime eliminates from the possible initial conditions those qubit states which would otherwise be mapped out of the Bloch sphere by the subsequent Markovian time evolution. By means of a simple model, we discuss some physical inconsistencies of this approach in relation to entanglement; in particular, we show that slipped nonpositive reduced dynamics might create entanglement through a purely local action.

DOI
10.1134/s1054660x06100021

Related papers

Redfield Reduced Dynamics and Entanglement

Sebastiano Anderloni, Fabio Benatti, Roberto Floreanini B

Abstract. In phenomenological applications the time evolution of subsystems immersed in an external environment are sometimes described by Markovian semigroups of Redfield type that result non-positive: the appearence of negative probabilities is avoided by restricting the admissible initial conditions to those states that remain positive under the action of the dynamics. We show that this often adopted procedure may lead to physical inconsistencies in presence of entanglement. Redfield Reduced Dynamics and Entanglement 2 1.

•Jan 1, 2007•12 citations

Redfield reduced dynamics and entanglement

Sebastiano Anderloni, Fabio Benatti, Roberto Floreanini B

In phenomenological applications, the time evolution of subsystems immersed in an external environment is sometimes described by Markovian semigroups of the Redfield type that have non-positive results: the appearance of negative probabilities is avoided by restricting the admissible initial conditions to those states that remain positive under the action of the dynamics. We show that this often adopted procedure may lead to physical inconsistencies in the presence of entanglement.

arXiv:quant-ph/0701157•Journal of Physics A Mathematical and Theoretical•Jan 30, 2007•13 citations

Local Generation of Entanglement with Redfield Dynamics

Fabio Benatti, Dariusz Chruściński, Roberto Floreanini B

In phenomenological applications, time evolutions of Bloch-Redfield type are widely adopted for modelling open system dynamics, despite their nonpositive preserving character: this physical inconsistency, that in general shows up at small times, is usually cured by suitably restricting the space of allowed initial states. Nevertheless, additional problems may arise in relation to entanglement: specifically, we show that Redfield dynamics, though being a semigroup, can generate entanglement through a purely local action; moreover, this unphysical effect can persist on long time-scales.

arXiv:2206.04508•Open Systems & Information Dynamics•Mar 1, 2022•5 citations

NON-POSITIVE SEMIGROUP DYNAMICS IN CONTINUOUS VARIABLE MODELS

Fabio Benatti, Roberto Floreanini B

Non-positive, Markovian semigroups are sometimes used to describe the time evolution of subsystems immersed in an external environment. A widely adopted prescription to avoid the appearance of negative probabilities is to eliminate from the admissible initial conditions those density matrices that would not remain positive by the action of the semigroup dynamics. Using a continuous variable model, we show that this procedure leads to physical inconsistencies when two subsystems are considered and their initial state is entangled.

arXiv:0705.3096•International Journal of Quantum Information•Feb 1, 2007•4 citations

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

Dynamics of two qubits in common 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 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.

Reviews in Mathematical Physics•Apr 28, 2020•3 citations
Nonpositive Markov approximations are sometimes used to describe the dynamics of qubits in weak interaction with suitable environments; the appearance of negative probabilities is avoided by assuming that the transient regime eliminates from the possible initial conditions those qubit states which would otherwise be mapped out of the Bloch sphere by the subsequent Markovian time evolution. By means of a simple model, we discuss some physical inconsistencies of this approach in relation to entanglement; in particular, we show that slipped nonpositive reduced dynamics might create entanglement through a purely local action.
Abstract. In phenomenological applications the time evolution of subsystems immersed in an external environment are sometimes described by Markovian semigroups of Redfield type that result non-positive: the appearence of negative probabilities is avoided by restricting the admissible initial conditions to those states that remain positive under the action of the dynamics. We show that this often adopted procedure may lead to physical inconsistencies in presence of entanglement. Redfield Reduced Dynamics and Entanglement 2 1.
In phenomenological applications, time evolutions of Bloch-Redfield type are widely adopted for modelling open system dynamics, despite their nonpositive preserving character: this physical inconsistency, that in general shows up at small times, is usually cured by suitably restricting the space of allowed initial states. Nevertheless, additional problems may arise in relation to entanglement: specifically, we show that Redfield dynamics, though being a semigroup, can generate entanglement through a purely local action; moreover, this unphysical effect can persist on long time-scales.
Non-positive, Markovian semigroups are sometimes used to describe the time evolution of subsystems immersed in an external environment. A widely adopted prescription to avoid the appearance of negative probabilities is to eliminate from the admissible initial conditions those density matrices that would not remain positive by the action of the semigroup dynamics. Using a continuous variable model, we show that this procedure leads to physical inconsistencies when two subsystems are considered and their initial state is entangled.
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.
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.