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arXiv:2108.01071 · Physical Review A

Time-extensive classical and quantum correlations in thermal machines

Milton Aguilar, Juan Pablo Paz

Published Jan 5, 2022• 3 citations
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Abstract

We study intraenvironmental classical and quantum correlations in a thermal machine, which is modeled as a driven quantum system coupled with thermal reservoirs. We compute the mutual information, the quantum discord, and the entanglement between two parts of the environment formed by oscillators centered around two different frequencies. We show that there are only two processes that generate time-extensive correlations in the long-time limit. First, there is a resonant process which is responsible for the transport of excitations between different environmental modes due to the absorption (or emission) of energy from (or into) the driving field. Second, there is a nonresonant process that transforms the energy from the external driving into pairs of excitations in two environmental modes. We show that there is a regime when the mutual information and the quantum discord between the parts of the environment correlated by these two processes grow quadratically in time, while entanglement production is time extensive.

DOI
10.1103/physreva.105.012410

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We study intraenvironmental classical and quantum correlations in a thermal machine, which is modeled as a driven quantum system coupled with thermal reservoirs. We compute the mutual information, the quantum discord, and the entanglement between two parts of the environment formed by oscillators centered around two different frequencies. We show that there are only two processes that generate time-extensive correlations in the long-time limit. First, there is a resonant process which is responsible for the transport of excitations between different environmental modes due to the absorption (or emission) of energy from (or into) the driving field. Second, there is a nonresonant process that transforms the energy from the external driving into pairs of excitations in two environmental modes. We show that there is a regime when the mutual information and the quantum discord between the parts of the environment correlated by these two processes grow quadratically in time, while entanglement production is time extensive.
We show that in a linear quantum machine, a driven quantum system that evolves while coupled with thermal reservoirs, entanglement between the reservoir modes is unavoidably generated. This phenomenon, which occurs at sufficiently low temperatures and is at the heart of the third law of thermodynamics, is a consequence of a simple process: the transformation of the energy of the driving field into pairs of excitations in the reservoirs. For a driving with frequency ${\ensuremath{\omega}}_{d}$ we show entanglement exists between environmental modes whose frequencies satisfy the condition ${\ensuremath{\omega}}_{i}+{\ensuremath{\omega}}_{j}={\ensuremath{\omega}}_{d}$. We show that this entanglement can persist for temperatures that can be significantly higher than the lowest achievable ones with sideband resolved cooling methods.
In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of continuous variable Gaussian Rényi-2 (GR2) quantum discord for a system consisting of two non-interacting non-resonant bosonic modes embedded in a thermal environment. In the case of both an entangled initial squeezed vacuum state and squeezed thermal state, GR2 quantum discord has non-negative values for all temperatures of the environment. We describe also the time evolution of GR2 classical correlations and GR2 quantum mutual information of the quantum system. All these quantities tend asymptotically to zero in the long time regime under the effect of the thermal bath.
In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of continuous variable quantum entanglement and quantum discord for a system consisting of two non-interacting non-resonant bosonic modes embedded in a thermal environment. We study the time evolution of logarithmic negativity, which characterizes the degree of entanglement, and show that in the case of an entangled initial squeezed thermal state, entanglement suppression takes place for all the temperatures of the environment, including zero temperature. We analyze the time evolution of the Gaussian quantum discord, which is a measure of all the quantum correlations in the bipartite state, including entanglement, and show that discord decays asymptotically in time under the effect of the thermal bath. We describe also the time evolution of classical correlations and quantum mutual information, which measures the total correlations of the quantum system.
In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of the continuous-variable quantum entanglement and quantum discord for a system consisting of two noninteracting modes embedded in a thermal environment. Entanglement and discord are used to quantify the quantum correlations of the system. For all values of the temperature of the thermal reservoir, an initial separable Gaussian state remains separable for all times. We study the time evolution of logarithmic negativity, which characterizes the degree of entanglement, and show that in the case of an entangled initial Gaussian state, entanglement suppression (entanglement sudden death) takes place, for non-zero temperatures of the environment. Only for a zero temperature of the thermal bath the initial entangled state remains entangled for finite times. We analyze the time evolution of the Gaussian quantum discord, which is a measure of all quantum correlations in the bipartite state, including entanglement, and show that quantum discord decays asymptotically in time under the effect of the thermal bath. This is contrast with the sudden death of entanglement. Before the suppression of the entanglement, the qualitative evolution of quantum discord is very similar to that of the entanglement. We describe also the time evolution of the degree of classical correlations and of quantum mutual information, which measures the total correlations of the quantum system.
In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of the continuous-variable quantum entanglement and quantum discord for a system consisting of two noninteracting modes embedded in a thermal environment. Entanglement and discord are used to quantify the quantum correlations of the system. For all values of the temperature of the thermal reservoir, an initially separable Gaussian state remains separable for all times. We study the time evolution of logarithmic negativity, which characterizes the degree of entanglement, and we show that in the case of an entangled initial Gaussian state, entanglement suppression (entanglement sudden death) takes place for non-zero temperatures of the environment. Only for zero temperature of the thermal bath the initial entangled state remains entangled for finite times. We analyze time evolution of Gaussian quantum discord, which is a measure of all quantum correlations in the bipartite state, including entanglement, and we show that quantum discord decays asymptotically in time under the effect of thermal bath. This is in contrast with the sudden death of entanglement. Before the suppression of entanglement, the qualitative evolution of quantum discord is very similar to that of the entanglement. We describe also time evolution of the degree of classical correlations and of quantum mutual information, which measures the total correlations of quantum system.
We study the harvesting of quantum and classical correlations from a hot scalar field in a periodic cavity by a pair of spatially separated oscillator-detectors. Specifically, we utilize nonperturbative and exact (non-numerical) techniques to solve for the evolution of the detectors-field system and then we examine how the entanglement, Gaussian quantum discord, and mutual information obtained by the detectors change with the temperature of the field. While (as expected) the harvested entanglement rapidly decays to zero as temperature is increased, we find remarkably that both the mutual information andandand the discord can actually be increased by multiple orders of magnitude via increasing the temperature. We go on to explain this phenomenon by a variety of means and are able to make accurate predictions of the behavior of thermal amplification. By doing this we also introduce a new perspective on harvesting in general and illustrate that the system can be represented as two dynamically decoupled systems, each with only a single detector. The thermal amplification of discord harvesting represents an exciting prospect for discord-based quantum computation, including its use in entanglement activation.