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:1705.07218 · Open Systems & Information Dynamics

Bath Energy for Correlated Initial States vs. Information Flow in Local Dephasing Channels

Filippo Giraldi

Published Jun 1, 2017• 3 citations
arXivHTMLPDF

Abstract

Variations of the bath energy are compared with the information flow in local dephasing channels. Special correlated initial conditions are prepared from the thermal equilibrium of the whole system, by performing a selective measurement on the qubit. The spectral densities under study are ohmic-like at low frequencies and include logarithmic perturbations of the power-law profiles. The bath and the correlation energy alternately increase or decrease, monotonically, over long times, according to the value of the ohmicity parameter, following logarithmic and power laws. Consider initial conditions such that the environment is in a thermal state, factorized from the state of the qubit. In the superohmic regime the long-time features of the information flow are transferred to the bath and correlation energy, by changing the initial condition from the factorized to the specially correlated, even with different temperatures. In fact, the low-frequency structures of the spectral density that provide information backflow with the factorized initial condition, induce increasing (decreasing) bath (correlation) energy with the specially correlated initial configuration. By performing the same change of initial conditions, the spectral properties providing information loss, produce decrease (increase) of the bath (correlation) energy.

DOI
10.1142/s1230161217500068

Related papers

Damped Oscillations of the Energy of a Bosonic Bath due to Spectral Gaps and Special Initial Correlations

Filippo Giraldi

The energy of the bosonic bath and the flow of quantum information in local dephasing channels are studied over short and long times in case the distribution of frequency modes of the bosonic bath exhibits a low-frequency gap. The initial conditions consist in special correlations between the qubit and the bosonic bath or are factorized, and involve thermal states of the whole system or of the bath. The low-frequency gap generates damped oscillations of the bath energy around the asymptotic value, for the correlated initial conditions, and induces the open system to alternately loose and gain information, for the factorized initial configurations. The long-time oscillations of the bath energy become regular and the frequency of the oscillations coincides with the upper cut-off frequency of the spectral gap. Regular long-time sequences of intervals are found over which the bath energy increases (decreases), for the correlated initial conditions, and information is lost (gained) by the open system, for the factorized initial configurations, even at different temperatures. This relation is reversed, if compared to the one obtained without the low-frequency gap, and can fail if the spectral density is tailored near the spectral gap according to power laws with odd natural powers.

arXiv:1707.00604•Open Systems & Information Dynamics•Sep 1, 2018•1 citation

Regular patterns in the information flow of local dephasing channels

Filippo Giraldi

Consider local dephasing processes of a qubit that interacts with a structured reservoir of frequency modes or a thermal bath, with Ohmic-like spectral density (SD). It is known that non-Markovian evolution appears uniquely above a temperature-dependent critical value of the Ohmicity parameter and non-Markovianity can be induced by properly engineering the external environment. In the same scenario, we find regular patterns in the flow of quantum information: Alternate directions appear in correspondence with periodic intervals of the Ohmicity parameter ${\ensuremath{\alpha}}_{0}$. The information flows back into the system over long times at zero temperature for $2+4n<{\ensuremath{\alpha}}_{0}<4+4n$, where $n=0,1,2,...,$ and at nonvanishing temperatures for $3+4n<{\ensuremath{\alpha}}_{0}<5+4n$. Under special conditions, backflow of information appears also for nonvanishing, even natural values of the Ohmicity parameter, at zero temperature, and for odd natural values at nonvanishing temperatures. Otherwise, the long-time information flows into the environment. In the transition from vanishing to arbitrary nonvanishing temperature, the long-time backflow of information is stable for $3+4n<{\ensuremath{\alpha}}_{0}<4+4n$, while it is reversed for $2+4n<{\ensuremath{\alpha}}_{0}<3+4n$ and $4+4n<{\ensuremath{\alpha}}_{0}<5+4n$. The patterns in the information flow are not altered if the low-frequency Ohmic-like profiles of the SDs are perturbed with additional factors that consist in arbitrary powers of logarithmic forms. Consequently, the flow of information can be controlled, directed, and reversed over long times by engineering a wide variety of reservoirs that includes and continuously departs from the Ohmic-like structure at low frequencies. Non-Markovianity and recoherence appear according to the same rules along with the backflow of information.

arXiv:1612.00813•Physical Review A•Feb 9, 2017•7 citations

Bath correlation functions for logarithmic-like spectral densities

Filippo Giraldi

We analyze the short- and long-time behavior of the bath correlation function for open quantum systems interacting with thermal baths. The spectral densities under study are ohmic-like at low frequencies, exhibit possible perturbations of the low-frequency power-law profiles and are arbitrarily shaped at higher frequencies. The low-frequency perturbations are provided by arbitrarily positive or negative powers of logarithmic forms as additional factors for the power laws of the ohmic-like spectral densities. If the spectral density decays sufficiently fast at high frequencies the short-time behavior of the bath correlation function is algebraic. The model provides long-time relaxations of the bath correlation function which are arbitrarily faster or slower than inverse power laws. In fact, the long-time relaxations are described by inverse power laws and by arbitrary powers of logarithmic forms as additional factors. Such relaxations are regularly related to the low-frequency structure of the spectral density, except for even or odd natural values of the ohmicity parameter. In these exceptional conditions the long-time relaxations of the bath correlation function are faster than those obtained via the regular relation.

International Journal of Quantum Information•Dec 1, 2017•5 citations

Survival of coherence for open quantum systems in thermal baths

Filippo Giraldi, Francesco Petruccione

The loss of coherence in a general open quantum system interacting with a bosonic environment is analyzed. The reservoir is initially in a thermal state. The reduced dynamics is described by a non-Markovian time-local master equation. We consider spectral densities that are sub- or super-Ohmic at low frequencies and arbitrarily shaped at high frequencies. In the super-Ohmic regime, for noninteger frequency powers larger than 2, long time survival of coherence appears. In the latter regime, at vanishing temperature, the asymptotic amount of surviving coherence is stabilized to its initial value, up to a phase factor, by properly increasing the bandwidth and decreasing the low-frequency profile of the spectral density. For noninteger positive frequency powers less than 2, stretched exponential-like decoherence is found over long times. The relaxations to the asymptotic configurations become arbitrarily slow by approaching the frequency power 2 of the super-Ohmic regime. The same dependence on temperature, spectral density, and scale frequency appears for purity and concurrence of two qubits and coherence of a qubit.

Physical Review A•Oct 2, 2013•14 citations

Sequences of information backflow in local dephasing channels with spectral gaps

Filippo Giraldi

The flow of quantum information in local dephasing channels is analyzed over short and long times in case the structured reservoir of frequency modes exhibits a spectral gap in the density of modes over low frequencies. The presence of the low-frequency gap with upper cut-off frequency [Formula: see text] produces an infinite sequence of long-time intervals over which information backflow appears. Though generally irregular, the time intervals exhibit, under certain conditions, upper bounds: the [Formula: see text]th episode of information backflow has already started at the instant [Formula: see text], and already ended at the instant [Formula: see text], for every [Formula: see text]. The intervals become regular over long times, tend to the asymptotic length [Formula: see text], as the supremum value, and are described analytically in terms of the structure of the spectral density near the upper cut-off frequency of the spectral gap. Consequently, engineering structured reservoirs of frequency modes with a spectral gap over low frequencies produces in local dephasing channels regular sequences of information backflow and recoherence over long times, along with non-Markovian evolution.

arXiv:1706.01163•International Journal of Quantum Information•Oct 1, 2017•3 citations

Effect of Cross-Spectral Correlations on Qubit Dynamics: Coherence Revival and Relaxation Modulation

Siddhartha Dutta, Sujay Mondal, Abhijit Bandyopadhyay

We investigate the reduced dynamics of a qubit subject to correlated longitudinal and transverse noise arising from its coupling to a shared bosonic bath. The environmental fluctuations are characterized by a positive-semidefinite matrix-valued spectral density, whose complex off-diagonal elements encode correlations between dephasing and relaxation channels in the frequency domain. Within the second-order time-convolutionless framework, we derive closed time-local equations for the Bloch-vector components of the reduced density matrix. The numerical implementation is validated against the exact pure-dephasing solution and the established behavior of the transverse-coupling spin-boson model. When both noise channels are present, the cross-spectral terms couple the otherwise distinct dephasing and relaxation sectors, producing dynamics that cannot be reproduced by adding independent noise contributions. In particular, the correlations generate non-monotonic population relaxation and a transient revival of coherence following its initial decay. The strength, bandwidth, delay, and phase of the cross spectrum provide control parameters for the magnitude and temporal structure of these effects. Our results demonstrate that correlated multi-axis noise can redistribute coherence loss and energy relaxation in time, thereby providing finite temporal windows of enhanced coherence or suppressed relaxation within the weak-coupling regime.

quant-pharXiv:2608.04672•Aug 6, 2026•0 citations
Variations of the bath energy are compared with the information flow in local dephasing channels. Special correlated initial conditions are prepared from the thermal equilibrium of the whole system, by performing a selective measurement on the qubit. The spectral densities under study are ohmic-like at low frequencies and include logarithmic perturbations of the power-law profiles. The bath and the correlation energy alternately increase or decrease, monotonically, over long times, according to the value of the ohmicity parameter, following logarithmic and power laws. Consider initial conditions such that the environment is in a thermal state, factorized from the state of the qubit. In the superohmic regime the long-time features of the information flow are transferred to the bath and correlation energy, by changing the initial condition from the factorized to the specially correlated, even with different temperatures. In fact, the low-frequency structures of the spectral density that provide information backflow with the factorized initial condition, induce increasing (decreasing) bath (correlation) energy with the specially correlated initial configuration. By performing the same change of initial conditions, the spectral properties providing information loss, produce decrease (increase) of the bath (correlation) energy.
The energy of the bosonic bath and the flow of quantum information in local dephasing channels are studied over short and long times in case the distribution of frequency modes of the bosonic bath exhibits a low-frequency gap. The initial conditions consist in special correlations between the qubit and the bosonic bath or are factorized, and involve thermal states of the whole system or of the bath. The low-frequency gap generates damped oscillations of the bath energy around the asymptotic value, for the correlated initial conditions, and induces the open system to alternately loose and gain information, for the factorized initial configurations. The long-time oscillations of the bath energy become regular and the frequency of the oscillations coincides with the upper cut-off frequency of the spectral gap. Regular long-time sequences of intervals are found over which the bath energy increases (decreases), for the correlated initial conditions, and information is lost (gained) by the open system, for the factorized initial configurations, even at different temperatures. This relation is reversed, if compared to the one obtained without the low-frequency gap, and can fail if the spectral density is tailored near the spectral gap according to power laws with odd natural powers.
Consider local dephasing processes of a qubit that interacts with a structured reservoir of frequency modes or a thermal bath, with Ohmic-like spectral density (SD). It is known that non-Markovian evolution appears uniquely above a temperature-dependent critical value of the Ohmicity parameter and non-Markovianity can be induced by properly engineering the external environment. In the same scenario, we find regular patterns in the flow of quantum information: Alternate directions appear in correspondence with periodic intervals of the Ohmicity parameter ${\ensuremath{\alpha}}_{0}$. The information flows back into the system over long times at zero temperature for $2+4n<{\ensuremath{\alpha}}_{0}<4+4n$, where n=0,1,2,...,n=0,1,2,...,n=0,1,2,..., and at nonvanishing temperatures for $3+4n<{\ensuremath{\alpha}}_{0}<5+4n$. Under special conditions, backflow of information appears also for nonvanishing, even natural values of the Ohmicity parameter, at zero temperature, and for odd natural values at nonvanishing temperatures. Otherwise, the long-time information flows into the environment. In the transition from vanishing to arbitrary nonvanishing temperature, the long-time backflow of information is stable for $3+4n<{\ensuremath{\alpha}}_{0}<4+4n$, while it is reversed for $2+4n<{\ensuremath{\alpha}}_{0}<3+4n$ and $4+4n<{\ensuremath{\alpha}}_{0}<5+4n$. The patterns in the information flow are not altered if the low-frequency Ohmic-like profiles of the SDs are perturbed with additional factors that consist in arbitrary powers of logarithmic forms. Consequently, the flow of information can be controlled, directed, and reversed over long times by engineering a wide variety of reservoirs that includes and continuously departs from the Ohmic-like structure at low frequencies. Non-Markovianity and recoherence appear according to the same rules along with the backflow of information.
We analyze the short- and long-time behavior of the bath correlation function for open quantum systems interacting with thermal baths. The spectral densities under study are ohmic-like at low frequencies, exhibit possible perturbations of the low-frequency power-law profiles and are arbitrarily shaped at higher frequencies. The low-frequency perturbations are provided by arbitrarily positive or negative powers of logarithmic forms as additional factors for the power laws of the ohmic-like spectral densities. If the spectral density decays sufficiently fast at high frequencies the short-time behavior of the bath correlation function is algebraic. The model provides long-time relaxations of the bath correlation function which are arbitrarily faster or slower than inverse power laws. In fact, the long-time relaxations are described by inverse power laws and by arbitrary powers of logarithmic forms as additional factors. Such relaxations are regularly related to the low-frequency structure of the spectral density, except for even or odd natural values of the ohmicity parameter. In these exceptional conditions the long-time relaxations of the bath correlation function are faster than those obtained via the regular relation.
The loss of coherence in a general open quantum system interacting with a bosonic environment is analyzed. The reservoir is initially in a thermal state. The reduced dynamics is described by a non-Markovian time-local master equation. We consider spectral densities that are sub- or super-Ohmic at low frequencies and arbitrarily shaped at high frequencies. In the super-Ohmic regime, for noninteger frequency powers larger than 2, long time survival of coherence appears. In the latter regime, at vanishing temperature, the asymptotic amount of surviving coherence is stabilized to its initial value, up to a phase factor, by properly increasing the bandwidth and decreasing the low-frequency profile of the spectral density. For noninteger positive frequency powers less than 2, stretched exponential-like decoherence is found over long times. The relaxations to the asymptotic configurations become arbitrarily slow by approaching the frequency power 2 of the super-Ohmic regime. The same dependence on temperature, spectral density, and scale frequency appears for purity and concurrence of two qubits and coherence of a qubit.
The flow of quantum information in local dephasing channels is analyzed over short and long times in case the structured reservoir of frequency modes exhibits a spectral gap in the density of modes over low frequencies. The presence of the low-frequency gap with upper cut-off frequency [Formula: see text] produces an infinite sequence of long-time intervals over which information backflow appears. Though generally irregular, the time intervals exhibit, under certain conditions, upper bounds: the [Formula: see text]th episode of information backflow has already started at the instant [Formula: see text], and already ended at the instant [Formula: see text], for every [Formula: see text]. The intervals become regular over long times, tend to the asymptotic length [Formula: see text], as the supremum value, and are described analytically in terms of the structure of the spectral density near the upper cut-off frequency of the spectral gap. Consequently, engineering structured reservoirs of frequency modes with a spectral gap over low frequencies produces in local dephasing channels regular sequences of information backflow and recoherence over long times, along with non-Markovian evolution.
We investigate the reduced dynamics of a qubit subject to correlated longitudinal and transverse noise arising from its coupling to a shared bosonic bath. The environmental fluctuations are characterized by a positive-semidefinite matrix-valued spectral density, whose complex off-diagonal elements encode correlations between dephasing and relaxation channels in the frequency domain. Within the second-order time-convolutionless framework, we derive closed time-local equations for the Bloch-vector components of the reduced density matrix. The numerical implementation is validated against the exact pure-dephasing solution and the established behavior of the transverse-coupling spin-boson model. When both noise channels are present, the cross-spectral terms couple the otherwise distinct dephasing and relaxation sectors, producing dynamics that cannot be reproduced by adding independent noise contributions. In particular, the correlations generate non-monotonic population relaxation and a transient revival of coherence following its initial decay. The strength, bandwidth, delay, and phase of the cross spectrum provide control parameters for the magnitude and temporal structure of these effects. Our results demonstrate that correlated multi-axis noise can redistribute coherence loss and energy relaxation in time, thereby providing finite temporal windows of enhanced coherence or suppressed relaxation within the weak-coupling regime.