Entanglement dynamics in two-mode Gaussian systems

Аурелиан Исар

Аурелиан Исар

Alina Stoica, Tatiana Mihaescu, Аурелиан Исар

Entanglement of formation is a measure that has a clear physically motivated definition, namely, it provides a lower bound over all pure-state entanglement decompositions required to create a given state. We investigate the open system dynamics of entanglement of formation of a two-mode Gaussian state interacting with a common bosonic environment. In the framework of the theory based on completely positive dynamical semigroups, the open system dynamics leads to a master equation in Lindblad form, which preserves the positivity and the Gaussian form of an initially Gaussian state at all times. For an initially separable state we witness the generation of entanglement, and its preservation in the limit of asymptotic times.

Аурелиан Исар

In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of the dynamics of entanglement for a system consisting of two uncoupled modes interacting with a thermal environment. Using Peres-Simon necessary and sufficient criterion of separability for two-mode Gaussian states, we describe the evolution of entanglement in terms of the covariance matrix for a Gaussian input state. We determine the asymptotic Gaussian maximally entangled mixed states (GMEMS) and their corresponding asymptotic maximal logarithmic negativity, which characterizes the degree of entanglement. Using the symplectic eigenvalues of the asymptotic covariance matrix, the expressions of von Neumann entropy and mutual information of asymptotic GMEMS are obtained.

Shao-Hua Xiang, Wei Wen, Zheng-Gang Shi +1 more

We use the symplectic transformation of the known linear optical elements to investigate the dynamical evolution of a three-mode cavityless optomechanical system and give explicit formulas for the input and output covariance matrices of the three mode fields when the initial state is Gaussian. Unlike the conventional approaches, the present one does not necessitate solution of the equation of motion of such a system. We study the dynamical behavior of bipartite entanglement in this system when the mirror vibrational mode is initially in a single-mode squeezed vacuum state and each of the two reflected optical sideband modes is in the vacuum state. It is found that the entanglement configuration alternates between a fully separable state and a continuous-variable entangled state during evolution.

Kiran K. Manne, Pranaw Rungta, Carlton M. Caves