Characterizing and quantifying quantum entanglement in states of open quantum systems are at the heart of quantum information theory. In this work, we study the mixedness and entanglement of a two-mode symmetrical Gaussian state evolving in a thermal Markovian environment. The considered state is that of two movable end-mirrors of two distant Fabry–Pérot cavities coupled via a two-mode squeezed light and driven by coherent lasers. We use the logarithmic negativity to consistently quantify the degree of entanglement between the two mechanical modes. The purity is employed as a witness of mixedness and characterize of entanglement in the two-mode mechanical bi-partition. By comparing the behavior of the logarithmic negativity with that of the purity under the effect of various parameters and based on the entanglement classification established in [G. Adesso, A. Serafini and F. Illuminati, Phys. Rev. Lett. 92, 087901 (2004)], we found that the purity can be used as a characterize and measure of entanglement in the two-mode symmetrical state when the squeezing parameter is fixed. The effects of thermal noise, squeezing and optomechanical coupling are also discussed in detail.
Characterizing and quantifying quantum entanglement in states of open quantum systems are at the heart of quantum information theory. In this work, we study the mixedness and entanglement of a two-mode symmetrical Gaussian state evolving in a thermal Markovian environment. The considered state is that of two movable end-mirrors of two distant Fabry–Pérot cavities coupled via a two-mode squeezed light and driven by coherent lasers. We use the logarithmic negativity to consistently quantify the degree of entanglement between the two mechanical modes. The purity is employed as a witness of mixedness and characterize of entanglement in the two-mode mechanical bi-partition. By comparing the behavior of the logarithmic negativity with that of the purity under the effect of various parameters and based on the entanglement classification established in [G. Adesso, A. Serafini and F. Illuminati, Phys. Rev. Lett. 92, 087901 (2004)], we found that the purity can be used as a characterize and measure of entanglement in the two-mode symmetrical state when the squeezing parameter is fixed. The effects of thermal noise, squeezing and optomechanical coupling are also discussed in detail.
We investigate the generation of quantum correlations between mechanical modes and optical modes in an optomechanical system, using the rotating wave approximation. The system is composed of two Fabry–Pérot cavities separated in space; each of the two cavities has a movable end-mirror. Our aim is the evaluation of entanglement between mechanical modes and optical modes, generated by correlations transfer from the squeezed light to the system, using Gaussian intrinsic entanglement as a witness of entanglement in continuous variables Gaussian states, and the quantification of the degree of mixedness of the Gaussian states using the purity. Then, we quantify nonclassical correlations between mechanical modes and optical modes even beyond entanglement by considering Gaussian geometric discord via the Hellinger distance. Indeed, entanglement, mixdness, and quantum discord are analyzed as a function of the parameters characterizing the system (thermal bath temperature, squeezing parameter, and optomechanical cooperativity). We find that, under thermal effect, when entanglement vanishes, purity and quantum discord remain nonzero. Remarkably, the Gaussian Hellinger discord is more robust than entanglement. The effects of the other parameters are discussed in detail.
The aim of this paper is to quantify the quantum correlations between mechanical and optical modes in an optomechanical system with two spatially separated Fabry–Pérot cavities. We use logarithmic negativity [Formula: see text] and entanglement of formation (EoF), respectively, to quantify entanglement between optical and mechanical modes, while Gaussian geometric discord (GGD) is used to capture all nonclassical correlations, including entanglement. These quantifiers are evaluated as functions of the physical parameters characterizing the environment and the system (the thermal bath temperature [Formula: see text], the photons number [Formula: see text], the optomechanical cooperativity [Formula: see text], the squeeze parameter [Formula: see text] and the drive pump power [Formula: see text]). By considering recent experimental parameters, we show that GGD is more robust than entanglement for high thermal bath temperature and low optomechanical cooperativity. We also find that these quantifiers improve with increasing optomechanical cooperativity. The effects of the other parameters are also discussed 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).
Abstract. Quantum entanglement of pure states of a bipartite system is defined as the amount of local or marginal (i.e. referring to the subsystems) entropy. For mixed states this identification vanishes, since the global loss of information about the state makes it impossible to distinguish between quantum and classical correlations. Here we show how the joint knowledge of the global and marginal degrees of information of a quantum state, quantified by the purities or in general by information entropies, provides an accurate characterization of its entanglement. In particular, for Gaussian states of continuous variable systems, we classify the entanglement of two–mode states according to their degree of total and partial mixedness, comparing the different roles played by the purity and the generalized p−entropies in quantifying the mixedness and bounding the entanglement. We prove the existence of strict upper and lower bounds on the entanglement and the existence of extremally (maximally and minimally) entangled states at fixed global and marginal degrees of information. This results allow for a powerful, operative method to measure mixedstate entanglement without the full tomographic reconstruction of the state. Finally, we briefly discuss the ongoing extension of our analysis to the quantification of multipartite entanglement in highly symmetric Gaussian states of arbitrary 1 × N-mode partitions. 1.
We study the dynamics of classical-quantum correlations in the nonadiabatic regime, using the rotating wave approximation (RWA), between two movable mirrors of two spatially separated Fabry–Pérot cavities, each of the two cavities having a movable end-mirror and coupled to a two-mode squeezed light from spontaneous parametric down-conversion. This work completes our previous work [M. Amazioug, M. Nassik and N. Habiballah, Eur. Phys. J. D 72, 171 (2018)] where we have studied the transfer of quantum correlations in steady state. The Bures distance is used to quantify the amount of entanglement of the symmetrical squeezed thermal state, and the Gaussian quantum discord is considered to quantify the quantumness of the quantum correlations even though the two movable mirrors are separable. Furthermore, total correlations are quantified using quantum mutual information. Indeed, these three indicators depend mainly on the temperature of the movable mirror and the squeezing parameter in strong coupling regime.
Quantum entanglement of pure states of a bipartite system is defined as the amount of local or marginal (i.e. referring to the subsystems) entropy. For mixed states this identification vanishes, since the global loss of information about the state makes it impossible to distinguish between quantum and classical correlations. Here we show how the joint knowledge of the global and marginal degrees of information of a quantum state, quantified by the purities or, in general, by information entropies, provides an accurate characterization of its entanglement. In particular, for Gaussian states of continuous variable systems, we classify the entanglement of two-mode states according to their degree of total and partial mixedness, comparing the different roles played by the purity and the generalized p-entropies in quantifying the mixedness and bounding the entanglement. We prove the existence of strict upper and lower bounds on the entanglement and the existence of extremally (maximally and minimally) entangled states at fixed global and marginal degrees of information. This results allow for a powerful, operative method to measure mixed-state entanglement without the full tomographic reconstruction of the state. Finally, we briefly discuss the ongoing extension of our analysis to the quantification of multipartite entanglement in highly symmetric Gaussian states of arbitrary 1 × N-mode partitions.