Narrow Results

We study the non-equilibrium dynamics of a disordered quantum system consisting of harmonic oscillators in a $d$-dimensional lattice. If the system is sufficiently localized, we show that, starting from a broad class of initial product states that are associated with a tiling (decomposition) of the $d$-dimensional lattice, the dynamical evolution of entanglement follows an area law in all times. Moreover, the entanglement bound reveals a dependency on how the subsystems are located within the lattice in dimensions $d\ge 2$. In particular, the entanglement grows with the maximum degree of the dual graph associated with the lattice tiling.

We investigate the quantum correlations of a two-qubit XYZ Heisenberg spin-1/2 chain model with Dzyaloshinskii–Moriya interaction. The two-qubit system is considered in thermal equilibrium. The variations of logarithmic negativity, uncertainty-induced quantum nonlocality (UIN) and trace distance discord, versus the parameters characterizing the system, are analyzed. The results show that the UIN measure captures quantum correlations that cannot be revealed by entanglement and trace discord. We also show that the Dzyaloshinskii–Moriya interaction enhances the non-classical correlations between the spins and can weaken the undesirable destructive effects of thermal fluctuations. In addition, an entangled–unentangled phase transition can be detected from the behavior of logarithmic negativity.

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 $(E_N)$ 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 $T$, the photons number $n_{\mathrm{\text{th}}}$, the optomechanical cooperativity $C$, the squeeze parameter $r$ and the drive pump power $P$). 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.

This investigation delves into the dynamics of quantum correlations and coherence within a two-dimensional electron gas (2DEG) system, taking into account the influence of Rashba spin–orbit coupling (SOC). We utilize metrics such as logarithmic negativity (${ℒ}{𝒩}$), local quantum uncertainty (LQU (${𝒰}$)), and relative entropy of coherence (${{𝒞}}_r$) to specifically assess these quantum resources among electron spins within non-interacting electron gases. Our study investigates how the separation distance (R) between electrons and the intensity of Rashba SOC ($\alpha$), impact the behavior of quantum properties within the 2DEG system. We find that specific strengths of Rashba SOC can effectively regulate quantum correlations and coherence within this system. Particularly significant is our observation that optimal quantum indicators emerge when electron proximity is minimized, underscoring the substantial influence of electron distance on quantum characteristics. Conversely, as electron separation increases, these quantum metrics diminish. Therefore, by adjusting the Rashba parameter, we can enhance the resilience of these quantum measurements against increasing electron separations, providing valuable insights into the potential for controlling and manipulating quantum behavior in similar 2DEG systems.

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.

In this paper, we investigate the pairwise quantum correlations in a two-qubit anisotropic Heisenberg model under the interplay of Calogero–Moser (CM) and Dzyaloshinsky–Moriya (DM) interactions in the presence of the homogeneous and inhomogeneous magnetic fields. We employ, respectively, the logarithmic negativity and local quantum uncertainty (LQU) to characterize the degree of entanglement and the amount of quantum correlations between the two parties of the considered system in equilibrium with a thermal reservoir. We analyze and compare the behaviors of the two quantum correlation quantifiers in the thermal state of the chain spin system and we discuss how relative distance between spins, equilibrium temperature, DM interaction coupling parameter and the external magnetic fields strengths influence the variations of both quantum correlation measures in such system.

We quantify and compare the quantum multipartite entanglement generated in two different physical systems involving parametric down-conversion of a multimode pumping field. In particular, we focus our attention on its scaling properties with respect to the number N of modes involved in the processes.

Lorentz transformation of the spin density matrix as well as the momentum density matrix for a quantum system of three massive spin-1/2 particles that have an appropriate discrete momentum distribution is investigated. In a rest frame, both the spin and the momentum parts are supposed to be maximally entangled as the Greenberger–Horne–Zeilinger state. Provided the particles move with sufficiently high speeds, we can find boosts that completely remove both the spin and momentum entanglements. We can even find boosts that completely preserve both entanglements. For the considered boosts, there is no mixing between the spin and the momentum parts.

We analyze an optomechanical system formed by a mechanical mode and the two optical modes of an optomechanical cavity for the realization of a strongly quantum correlated three-mode system. We show that the steady state of the system shows three possible bipartite continuous variable (CV) entanglements in an experimentally accessible parameter regime, which are robust against temperature. We further show that selective entanglement between the mechanical mode and any of the two optical modes is also possible by the proper choice of the system parameters. Such a two-mode optomechanical system can be used for the realization of CV quantum information interfaces and networks.

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.

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.

We investigate the dynamics of entanglement, uncertainty and mixedness by solving time-dependent Schrödinger equation for two-dimensional harmonic oscillator with time-dependent frequency and coupling parameter subject to a static magnetic field. We compute the purities (global/marginal) and then calculate explicitly the linear entropy $S_L$ as well as logarithmic negativity ${𝒩}$ using the symplectic parametrization of vacuum state. We introduce the spectral decomposition to diagonalize the marginal state and get the expression of von Neumann entropy $S_{\mathrm{\text{von}}}$ and establish its link with $S_L$. We use the Wigner formalism to derive the Heisenberg uncertainties and show their dependencies on both $S_L$ and the coupling parameters ${\gamma }_i$$(i=1,2)$ of the quadrature term $x_i{p}_i$. We graphically study the dynamics of the three features (entanglement, uncertainty, mixedness) and present a similar topology with respect to time. We show the effects of the magnetic field and quenched values of $J(t)$ and ${\omega }_2(t)$ on these three dynamics, which lead eventually to control and handle them.

We describe the evolution of the quantum entanglement in a system composed of two interacting bosonic modes immersed in a thermal reservoir, in the framework of the theory of open systems based on completely positive quantum dynamical semigroups. The evolution of entanglement is described in terms of the covariance matrix for Gaussian initial states. We calculate the logarithmic negativity and show that for separable initial squeezed thermal states entanglement generation may take place, for definite values of squeezing parameter, average photon numbers, temperature of the thermal bath, dissipation constant and the strength of interaction between the two modes. After its generation one can observe temporary suppressions and revivals of the entanglement. For entangled initial squeezed thermal states, entanglement suppression takes place, for all temperatures of the reservoir, and temporary revivals and suppressions of entanglement can be observed too. In the limit of infinite time the system evolves asymptotically to an equilibrium state which may be entangled or separable.

One cannot always obtain information about entanglement by the Dür–Cirac (DC) method. The impracticality is attributed to the decrease of entanglement by local operations in the DC method. Even in 2–qubit systems, there exist states whose entangled property the DC method never evaluates. This result is closely related to the discussion of purification protocols. In addition, we discuss its effectiveness in multiqubit systems.