Minkowski structure for purity and entanglement of Gaussian bipartite states

Abstract

The relation between the symplectic and Lorentz groups is explored to investigate entanglement features in a two-mode bipartite Gaussian state. We verify that the correlation matrix of arbitrary Gaussian states can be associated to a hyperbolic space with a Minkowski metric, which is divided in two regions - separablelike and entangledlike, in equivalence to timelike and spacelike in special relativity. This correspondence naturally allows the definition of two insightful invariant squared distances measures - one related to the purity and another related to amount of entanglement. The second distance allows us to define a measure for entanglement in terms of the invariant interval between the given state and its closest separable state, given in a natural manner without the requirement of a minimization procedure.

5 pages, 4 figures

References in corpus (3)

• Symplectic invariants, entropic measures and correlations of Gaussian states
• Entanglement of formation for an arbitrary two-mode Gaussian state
• Entanglement, Purity, and Information Entropies in Continuous Variable Systems

Cited by in corpus (1)

• Capacitive Coupling of Two Transmission Line Resonators Mediated by the Phonon Number of a Nanoelectromechanical Oscillator