We formulate an inseparability criterion based on the recently derived generalized Schrödinger–Robertson uncertainty relation (SRUR) [J. Phys. A 45, 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.
© 2014 Optical Society of America
Original Manuscript: December 5, 2013
Manuscript Accepted: January 20, 2014
Published: March 3, 2014
Chang-Woo Lee, Junghee Ryu, Jeongho Bang, and Hyunchul Nha, "Inseparability criterion using higher-order Schrödinger–Robertson uncertainty relation," J. Opt. Soc. Am. B 31, 656-663 (2014)