Negativity of asymmetric two-mode Gaussian states: An explicit analytic formula and physical interpretation

摘要

We show that the negativity of a general two-mode Gaussian state can be explicitly expressed in terms of an optimal uncertainty product in position-momentum space. Such an uncertainty product is shown to have the greatest violation of a separability criterion based on positive partial transposition. Our analytic formula indicates the observables determining the negativity. For asymmetric Gaussian states, we show that the negativity is controlled by an asymmetric parameter which sets an upper bound for the negativity.