For every two-mode Gaussian state, the unrestricted entanglement of formation equals its Gaussian restriction, resolving the two-mode instance of Open Quantum Problem 29.
Entanglement of Formation for Gaussian States
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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 {\em et al} [Phys. Rev. Lett. {\bf 91}, 107901 (2003)], to noncommuting variables. The conjecture itself is in respect of an extremal property of this generalized EPR correlation.
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Optimality of Gaussian Entanglement of Formation
For every two-mode Gaussian state, the unrestricted entanglement of formation equals its Gaussian restriction, resolving the two-mode instance of Open Quantum Problem 29.