Entanglement of formation for Gaussian states

Abstract

The entanglement of formation (EOF) is computed for arbitrary two-mode Gaussian states. Apart from a conjecture, our analysis rests on two main ingredients. The first is a four-parameter canonical form we develop for the covariance matrix, one of these parameters acting as a measure of EOF, and the second is a generalisation of the EPR correlation, used in the work of Giedke et al [Phys. Rev. Lett. 91, 107901 (2003)], to noncommuting variables. The conjecture itself is in respect of an extremal property of this generalized EPR correlation.