Inseparability criterion using higher-order Schrödinger–Robertson uncertainty relation
Chang-Woo Lee, Junghee Ryu, Jeongho Bang, Hyunchul Nha · Journal of the Optical Society of America B · 2014
We formulate an inseparability criterion based on the recently derived generalized Schrödinger–Robertson uncertainty relation (SRUR) [J. Phys. A45, 195305 (2012)] together with the negativity of partial transpose (PT). This generalized SRUR systematically deals with two orthogonal quadrature amplitudes to higher orders, so it is relevant to characterize non-Gaussian quantum statistics. We first present a method that relies on the single-mode marginal distribution of two-mode fields under PT followed by beam-splitting operation. We then extend the SRUR to two-mode cases and develop a full two-mode version of the inseparability criterion. We find that our formulation can be useful to detect entanglement of non-Gaussian states even when, e.g., the entropic criterion that also involves higher-order moments fails.