Evolution and entanglement of Gaussian states in the parametric amplifier

Abstract

The linear time-dependent constants of motion of the parametric amplifier are obtained and used to determine in the tomographic-probability representation the evolution of a general two-mode Gaussian state. By means of the discretization of the continuous variable density matrix, the von Neumann and linear entropies are calculated to measure the entanglement properties between the modes of the amplifier. The obtained results for the nonlocal correlations are compared with those associated to a linear map of discretized symplectic Gaussian-state tomogram onto a qubit tomogram. This qubit portrait procedure is used to establish Bell-type's inequalities, which provide a necessary condition to determine the separability of quantum states, which can be evaluated through homodyne detection. Other no-signaling nonlocal correlations are defined through the portrait procedure for noncomposite systems.

References in corpus (7)

• Bell nonlocality
• Entanglement detection
• Towards higher precision and operational use of optical homodyne tomograms
• Beyond spectral homodyne detection: complete quantum measurement of spectral modes of light
• Tomographic test of Bell's inequality for a time-delocalized single photon
• Qubit portrait of the photon-number tomogram and separability of two-mode light states
• Squeezing Operator and Squeeze Tomography

Cited by in corpus (3)

• Differential Parametric Formalism for the Evolution of Gaussian States: Nonunitary Evolution and Invariant States
• Symplectic tomographic probability distribution of crystallized Schrödinger cat states
• Discretization of the density matrix as a nonlinear positive map and entanglement