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Chinese Physics B

Dynamics and resilience of quantum correlations between two-mode Gaussian states in Gaussian environments

Y. Lahlou, M. Amazioug, Bouchra Maroufi, Mohammed Daoud A

Published Oct 28, 2026• 0 citations
Publisher

Abstract

Abstract Gaussian states, characterized by probability distributions in phase-space representations, play a fundamental role in quantum information processing. Despite their mathematical tractability, the presence of noise imposes limitations on achieving quantum protocols, impacting their effectiveness in continuous-variable quantum systems for various communication and computation tasks. Hence, investigating quantum entanglement and quantum correlations within the coherence of Gaussian states in noisy channels holds significant importance. In this study, we introduce and investigate a framework designed to precisely define and explore the dynamic evolution of quantum correlations within twomode Gaussian states subjected to the effects of a Gaussian thermal environment. We elucidate the temporal progression of quantum correlations within an open system comprising two interconnected bosonic modes embedded in a Gaussian thermal environment. We explore the impact of the environment by considering the evolution of the initial parameters of the input states. We measure the quantum correlations by employing the quantifiers: the Gaussian logarithmic negativity (GLN) N and the Gaussian quantum discord (GQD) D G . The behavior of these quantum correlation quantifiers is intricately related to the parameters of the input states utilized in the analysis. We demonstrate that the GQD D G serves as an appropriate measurement quantifier in capturing fundamental quantum correlations, outperforming other quantifiers. Furthermore, our findings reveal that the GQD D G exhibits greater resilience compared to GLN N , showing a reduced sensitivity to external influences.

DOI
10.1088/1674-1056/aeba5f

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Abstract Gaussian states, characterized by probability distributions in phase-space representations, play a fundamental role in quantum information processing. Despite their mathematical tractability, the presence of noise imposes limitations on achieving quantum protocols, impacting their effectiveness in continuous-variable quantum systems for various communication and computation tasks. Hence, investigating quantum entanglement and quantum correlations within the coherence of Gaussian states in noisy channels holds significant importance. In this study, we introduce and investigate a framework designed to precisely define and explore the dynamic evolution of quantum correlations within twomode Gaussian states subjected to the effects of a Gaussian thermal environment. We elucidate the temporal progression of quantum correlations within an open system comprising two interconnected bosonic modes embedded in a Gaussian thermal environment. We explore the impact of the environment by considering the evolution of the initial parameters of the input states. We measure the quantum correlations by employing the quantifiers: the Gaussian logarithmic negativity (GLN) N and the Gaussian quantum discord (GQD) D G . The behavior of these quantum correlation quantifiers is intricately related to the parameters of the input states utilized in the analysis. We demonstrate that the GQD D G serves as an appropriate measurement quantifier in capturing fundamental quantum correlations, outperforming other quantifiers. Furthermore, our findings reveal that the GQD D G exhibits greater resilience compared to GLN N , showing a reduced sensitivity to external influences.
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 temperatures of the environment, including zero temperature. 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 discord decays asymptotically in time under the effect of the thermal bath. We describe also the time evolution of classical correlations.
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.
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.
Gaussian noise channels arise naturally in many physical situations and play an important role in information transmission involving continuous-variable quantum systems. In this work we employ Gaussian noise channels to probe and characterize correlations in two-mode bosonic fields. Based on the fact that local channels often cause more decoherence for global states than for local states due to correlations, we introduce a notion of conditional coherence relative to a local channel, which is defined as the difference between the global and local decoherence caused by the channel. We discuss its connections with quantum discord and relative quantum Fisher information and propose a class of correlation quantifiers for two-mode bosonic states in terms of conditional coherence relative to local Gaussian noise channels. We prove that any nonproduct state exhibits such correlations and show that these correlation quantifiers are measures of total correlations, which may include both classical and quantum parts. We further illustrate these correlation quantifiers through several typical two-mode bosonic states and make a comparative study between these correlation quantifiers and other known ones such as entanglement and discord.
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. 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.