In a two-mode Gaussian state [Formula: see text], we report on stationary evolution of three measures of correlations defined via the Rényi-2 entropy, i.e. quantum mutual information (QMI) [Formula: see text], the Gaussian–Rényi-2 entanglement (GR2E) [Formula: see text] and Gaussian quantum steering (GQS) [Formula: see text]. We evaluate analytical expression of the covariance matrix fully describing the state [Formula: see text]. Further, we study, under influences of parameters characterizing the state at hand and its environment, the behavior of the three considered measures. We find that quantum steering [Formula: see text] is always upper bounded by (GR2E) [Formula: see text], which in turn is found always upper bounded by half of the QMI [Formula: see text]. This therefore satisfies the hierarchical relation [Formula: see text] established in [L. Lami, C. Hirche, G. Adesso and A. Winter, Phys. Rev. Lett. 117 (2016) 220502]. Importantly, we find that both GR2E [Formula: see text] and GQS [Formula: see text] are strongly affected by the thermal effects. Remarkably, when the GR2E [Formula: see text] thoroughly vanishes, the GMI [Formula: see text] exhibits a freezing behavior, and seems to be captured within a wide range of temperature.
In a two-mode Gaussian state [Formula: see text], we report on stationary evolution of three measures of correlations defined via the Rényi-2 entropy, i.e. quantum mutual information (QMI) [Formula: see text], the Gaussian–Rényi-2 entanglement (GR2E) [Formula: see text] and Gaussian quantum steering (GQS) [Formula: see text]. We evaluate analytical expression of the covariance matrix fully describing the state [Formula: see text]. Further, we study, under influences of parameters characterizing the state at hand and its environment, the behavior of the three considered measures. We find that quantum steering [Formula: see text] is always upper bounded by (GR2E) [Formula: see text], which in turn is found always upper bounded by half of the QMI [Formula: see text]. This therefore satisfies the hierarchical relation [Formula: see text] established in [L. Lami, C. Hirche, G. Adesso and A. Winter, Phys. Rev. Lett. 117 (2016) 220502]. Importantly, we find that both GR2E [Formula: see text] and GQS [Formula: see text] are strongly affected by the thermal effects. Remarkably, when the GR2E [Formula: see text] thoroughly vanishes, the GMI [Formula: see text] exhibits a freezing behavior, and seems to be captured within a wide range of temperature.
This work reports on the stationary evolution of three different kinds of quantum correlations between two distant magnon modes. The system at hand consists of two spatially separated cavities, where each cavity has a microwave (MW) cavity and a magnon mode. The two cavities are coupled to each other via the photon-tunneling process, and both are exposed to the output field of a squeezed vacuum MW fields source. By calculating the covariance matrix fully describing the state of the two magnon modes, we give the explicit expressions of the measures of correlations defined via the Rényi-2 entropy, i.e. the Gaussian quantum steering [Formula: see text], Gaussian Rényi-2 entanglement [Formula: see text] and Gaussian Rényi-2 mutual information [Formula: see text]. We find that, the quantum steering is always upper bounded by the entanglement, which is in turn always upper bounded by half of the total correlations. The obtained results are consistent with the hierarchical Rényi-2 quantum correlations established in [L. Lami, C. Hirche, G. Adesso and A. Winter, Phys. Rev. Lett. 117, 220502 (2016)], i.e. they fulfill the hierarchical inequality [Formula: see text]. The influences of the squeezing parameter, the environmental temperature, the cavity–magnon coupling and the cavity–cavity coupling on the correlations are studied in detail.
Abstract We report on temporal evolution of three different kinds of correlations present between two mechanical resonators of two distant Fabry-Pérot cavities. The two cavities are jointly fed by a two-mode squeezed light and driven by two independent coherent lasers. We consider the initial state of the two mechanical modes as a two-mode uncorrelated thermal state. After evaluating the dynamical covariance matrix elements, we give explicit expressions of the measures of correlations defined via the Rényi-2 entropy, namely, the Rényi-2 quantum mutual information, the Gaussian Rényi-2 entanglement and the Gaussian quantum steering. We find that by an appropriate choice of the system parameters, it is possible to generate entanglement and steering via a quantum correlations transfer from squeezed light to the mechanical bi-mode state. The influence of the squeezing parameter, the optomechanical cooperativity and the environmental thermal noise on the correlations are studied thoroughly. Additionally, we show in various circumstances that the considered temporal correlations respect the hierarchical relation established in L Lami, C Hirche, G Adesso, and A Winter, (2016 Phys. Rev. Lett. 117 , 220 502).
In this paper, we investigate, in the framework of the theory of open quantum systems, based on completely positive dynamical semigroups, the Markovian dynamics of Gaussian Rényi-2 correlations — quantum entanglement, quantum discord, mutual information and classical correlations in a system composed of two bosonic modes, interacting with a squeezed thermal bath. We show that the time evolution of the Rényi-2 correlations strongly depends on the parameters of the initial Gaussian squeezed thermal state of the considered system and on the parameters characterizing the squeezed thermal bath. It is shown that while Gaussian Rényi-2 entanglement is suppressed in a finite time, due to the interaction with the squeezed thermal bath, the correlations beyond entanglement — Gaussian Rényi-2 discord, classical correlations and mutual information undergo a freezing-like behavior, namely they decay only asymptotically, in the limit of large times. We also illustrate a fundamental hierarchy for bipartite Gaussian correlations.
Using the Gaussian Rényi-2 entropy, we analyse the behaviour of two different aspects of quantum correlations (entanglement and quantum discord) in two optomechanical subsystems (optical and mechanical). We work in the resolved sideband and weak coupling regimes. In experimentally accessible parameters, we show that it is possible to create entanglement and quantum discord in the considered subsystems by quantum fluctuations transfer from either light to light or light to matter. We find that both mechanical and optical entanglement are strongly sensitive to thermal noises. In particular, we find that the mechanical one is more affected by thermal effects than that optical. Finally, we reveal that under thermal noises, the discord associated with the entangled state decays aggressively, whereas the discord of the separable state (quantumness of correlations) exhibits a freezing behaviour, seeming to be captured over a wide range of temperature.
Quantum mutual information is a fundamental quantity for characterizing correlations among quantum systems. In this work, we investigate the dynamic evolution of the quantum mutual information based on Rényi-2 entropy for three-mode Gaussian states in the background of a Schwarzschild black hole. We find that the physically inaccessible mutual information increases with Hawking temperature and eventually saturates, while the physically accessible mutual information exhibits nonmonotonic temperature dependence: it first rises, reaches a peak, then declines toward a finite asymptotic value. This nonmonotonic behavior differs from the monotonic degradation typically observed for Gaussian entanglement and steering in curved spacetime. Furthermore, we establish several constraint relations governing the distribution of mutual information among subsystems. These findings contribute to understanding the quantumness of quantum correlations for continuous variable in Schwarzschild spacetime.
Quantum correlations play a fundamental role in quantum information science. Within bipartite mixed states, they can arise in different incarnations, i.e. Bell nonlocality, steering, and entanglement. Besides being of fundamental interest, they can all be exploited to attain enhancements in quantum information processing tasks over classical methods. Here, in a two-mode Gaussian state [Formula: see text], where the mode [Formula: see text]([Formula: see text]) is generated during the first(second) transition of a correlated-emission laser, we perform a comparative study between the three forms of quantum correlations in the presence of dissipation and thermal noise. We use the master equation of the state [Formula: see text] to obtain the first and second moments of the laser modes variables in the steady state regime. Under realistic experimental conditions, we show that Bell nonlocality could be exhibited by the state [Formula: see text] only when the two laser modes [Formula: see text] and [Formula: see text] are weakly entangled, in contrast, it disappears when they are strongly entangled. Especially, we find that Bell nonlocality is strongly sensitive to thermal noise. Also, we show that the state [Formula: see text] can display one-way and two-way steering in a wide range of operating parameters. In particular, we demonstrate that one-way steering can be detected solely in the direction [Formula: see text]. Against thermal noise, entanglement is found to be more robust than steering, which is in turn found to be more robust than Bell nonlocality. The obtained results are helpful in understanding the behavior of quantum nonlocality in dissipative-noisy environments, and may find potential applications for quantum information tasks.