A Computable Gaussian Quantum Correlation for Continuous-Variable Systems

Generally speaking, it is difficult to compute the values of the Gaussian quantum discord and Gaussian geometric discord for Gaussian states, which limits their application. In the present paper, for any (n+m)-mode continuous-variable system, a computable Gaussian quantum correlation M is proposed. For any state ρAB of the system, M(ρAB) depends only on the covariant matrix of ρAB without any measurements performed on a subsystem or any optimization procedures, and thus is easily computed. Furthermore, M has the following attractive properties: (1) M is independent of the mean of states, is symmetric about the subsystems and has no ancilla problem; (2) M is locally Gaussian unitary invariant; (3) for a Gaussian state ρAB, M(ρAB)=0 if and only if ρAB is a product state; and (4) 0≤M((ΦA⊗ΦB)ρAB)≤M(ρAB) holds for any Gaussian state ρAB and any Gaussian channels ΦA and ΦB performed on the subsystem A and B, respectively. Therefore, M is a nice Gaussian correlation which describes the same Gaussian correlation as Gaussian quantum discord and Gaussian geometric discord when restricted on Gaussian states. As an application of M, a noninvasive quantum method for detecting intracellular temperature is proposed.

Dynamics of classical-quantum correlations between two movable mirrors in optomechanics

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 coherence versus nonclassical correlations in optomechanics

Coherence arises from the superposition principle, where it plays a central role in quantum mechanics. In Phys. Rev. Lett. 114, 210401 (2015), it has been shown that the freezing phenomenon of quantum correlations beyond entanglement is intimately related to the freezing of quantum coherence (QC). In this paper, we compare the behavior of entanglement and quantum discord with quantum coherence in two different subsystems (optical and mechanical). We use respectively the entanglement of formation (EoF) and the Gaussian quantum discord (GQD) to quantify entanglement and quantum discord. Under thermal noise and optomechanical coupling effects, we show that EoF, GQD and QC behave in the same way. Remarkably, when entanglement vanishes, GQD and QC remain almost unaffected by thermal noise, keeping nonzero values even for high-temperature, which is in concordance with Phys. Rev. Lett. 114, 210401 (2015). Also, we find that the coherence associated with the optical subsystem is more robust — against thermal noise — than those of the mechanical subsystem. Our results confirm that optomechanical cavities constitute a powerful resource of QC.

Quantum Correlation Based on Uhlmann Fidelity for Gaussian States

A quantum correlation N F G , A for ( n + m ) -mode continuous-variable systems is introduced in terms of local Gaussian unitary operations performed on Subsystem A based on Uhlmann fidelity F. This quantity is a remedy for the local ancilla problem associated with the geometric measurement-induced correlations; is local Gaussian unitary invariant; is non-increasing under any Gaussian quantum channel performed on Subsystem B;and is an entanglement monotone when restricted to pure Gaussian states in the ( 1 + m ) -mode case. A concrete formula for ( 1 + 1 ) -mode symmetric squeezed thermal states (SSTSs) is presented. We also compare N F G , A with other quantum correlations in scale, such as Gaussian quantum discord and Gaussian geometric discord, for two-mode SSTSs, which reveals that N F G , A has some advantage in detecting quantum correlations of Gaussian states.

Measure of general quantum correlations in optomechanics

In this paper, we analyze nonclassical correlations between bipartite states in two optomechanical systems. The first system (Sec. 2) consists of two nanoresonators spatially separated by broadband squeezed light, where each cavity has a fixed mirror and a movable one. The second system (Sec. 3) is an atom-optomechanical system consisting of an atomic ensemble placed inside an optical nanoresonator with a vibrating mirror. For both optomechanical systems, we give the Hamiltonian and the explicit expression of covariance matrix leading to the quantum equations describing the dynamic evolution of the system. Then, the nonclassical correlations are quantified using the logarithmic negativity and Gaussian quantum discord. We propose also a scheme for examining the evolution of Gaussian quantum steering and its asymmetry in each system. We show that the entanglement of the two mechanical modes is very strongly related to the parameters characterizing the environment where the movable mirrors evolve, in particular the squeeze parameter, the optomechanical cooperativity and thermal bath temperature.

Entanglement versus Gaussian quantum discord in a double-cavity opto-mechanical system

In this paper, we investigate the robustness of the quantum correlations against the environment effects in various opto-mechanical bipartite systems. For two spatially separated opto-mechanical cavities, we give analytical formula for the global covariance matrix involving two mechanical modes and two optical modes. The logarithmic negativity as an indicator of the degree of entanglement and the Gaussian quantum discord which is a witness of quantumness of correlations are used as quantifiers to evaluate the different pairwise quantum correlations in the whole system. The evolution of the quantum correlations existing in this opto-mechanical system are analyzed in terms of the thermal bath temperature, squeezing parameter and the opto-mechanical cooperativity. We find that with desirable choice of these parameters, it is possible either to enhance or annihilate the quantum correlations in the system. Various scenarios are discussed in detail.

Dynamic of the Gaussian quantum discord and effect of non-Markovian degree

We study the dynamic of the Gaussian quantum discord in a continuous-variable system subject to a common non-Markovian environment with zero-temperature. By considering an initial two-mode Gaussian symmetric squeezed thermal state, we show that Gaussian discord has a very different dynamic characteristic in a non-Markovian evolution versus a Markov process, and can be created by the memory effect, which features non-Markovianity. We also study the relationship between Gaussian discord and the non-Markovian degree of the environment. The results may offer us an effective experimental method to get more quantum correlations.