Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Complex amplification and non-symmetric amplitude damping of two-mode Gaussian state

Li-xhen Jiang

Published Oct 26, 2007• 0 citations

Abstract

The evolution of two-mode Gaussian state under complex amplification, non-symmetric damping and thermal noise is studied. The analytical time dependent solution of the state characteristic function is obtained in some special cases. The separability criterions are given for the final state of weak complex amplification as well as strong complex amplification.

DOI: 10.1117/12.754811

Related papers

The separability of two-mode Gaussian state under amplification and symmetric damping

Xiaoyu Chen, Li-zhen Jiang, Liang-neng Wu

The performances of a two-mode Gaussian state under parametric amplification, symmetric amplitude damping and thermal noise are studied. The time-dependent complex correlation matrix of the state in evolution is given. The separability of the final two-mode Gaussian state is examined under symmetric amplification and asymmetric amplification separately.

arXiv:0710.2570Chinese PhysicsAug 1, 20070 citations

The separability of tripartite Gaussian states with amplification and amplitude damping

Xiaoyu Chen

The most general evolution solution of multi-mode continuous variable states is given when it undergoes amplification, amplitude damping and thermal noise. In the case of some kind of initial Gaussian state totally symmetrically interacting with the environment, the conditions for full separability and full entanglement of the final tripartite three-mode Gaussian state are worked out.

Journal of Physics A Mathematical and TheoreticalApr 2, 20080 citations

The separability of the evolved tripartite Gaussian state

Xiaoyu Chen

We consider the time evolution of the tripartite three mode Gaussian state which is initially prepared in genuine entangled pure state. The state undergoes parametric amplification and amplitude damping as well as thermal noise. The correlation matrix of the evolved state is studied in the symmetrical case. The separability conditions are given.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIEOct 26, 20070 citations

Simultaneous amplitude and phase damping of x−p symmetric Gaussian states and their separability

Xiaoyu Chen

We give the time evolution solution of simultaneous amplitude and phase damping for any continuous variable state. For the simultaneous amplitude and phase damping of two-mode $x\text{\ensuremath{-}}p$ symmetric entangled Gaussian states, two analytical conditions of the separability are given. One is the sufficient condition of separability. The other is the condition of positive partial transpose (PPT) separability where the Peres-Horodecki criterion is applied. Between the two conditions there may exist bound entanglement. The simplest example is the simultaneous amplitude and phase damping of a two-mode squeezed vacuum state. The damped state is non-Gaussian.

arXiv:quant-ph/0508209Physical Review AFeb 2, 200618 citations

The characteristic function and entanglement of optical evolution

Xiaoyu Chen

The master equation of the quantum optical density operator is transformed to the equation of the characteristic function. Parametric amplification and amplitude damping as well as phase damping are considered. The solution for the most general initial quantum state is obtained for parametric amplification and amplitude damping. The purity of the one-mode Gaussian system and the entanglement of the two-mode Gaussian system are studied.

arXiv:quant-ph/0604208Journal of Physics B Atomic Molecular and Optical PhysicsOct 27, 20069 citations

Separability dynamics of two-mode Gaussian states in parametric conversion and amplification

Alexandre V. Dodonov, V. V. Dodonov, Salomon Sylvain Mizrahi

We give a simplified form of Simon's separability criterion for two-mode Gaussian states, showing that for systems whose unitary evolution is governed by arbitrary time-dependent quadratic Hamiltonians, the separability dynamics is completely described in terms of the determinant of the cross-covariance matrix. As concrete examples, we consider the evolution of the 'inverse negativity coefficient' (which gives a quantitative estimation of the 'degree of entanglement') for two initially uncoupled modes (each being in a squeezed thermal state) in the cases of parametric converter, parametric amplifier and for a cavity whose boundary oscillates in resonance with two field modes.

Journal of Physics A Mathematical and GeneralDec 24, 200452 citations