Research Specifications

We define an EPR-like uncertainty by using the Duan et al.’s inequality which gives a necessary and sufficient condition for the separability of any two-mode Gaussian state. We show that for a given amount of entanglement, the uncertainty is minimized by pure two-mode squeezed states. Using this fact, we write the optimal pure-state decomposition and derive a compact form for the entanglement of formation of two-mode Gaussian states.We succeed to prove the conjecture proposed by Simon et al. and also show that for two-mode Gaussian states, the entanglement of formation coincides with the Gaussian entanglement of formation. For illustration purposes, we consider symmetric and squeezed thermal states as special cases and evaluate their entanglement of formation explicitly. Our results are in agreement with the Giedke et al.’s and Marians’s ones, respectively.