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arXiv:1403.2172 · Journal of the Optical Society of America B

Inseparability criterion using higher-order Schrödinger–Robertson uncertainty relation

Chang-Woo Lee, Junghee Ryu, Jeongho Bang, Hyunchul Nha

Published Mar 3, 2014• 6 citations
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Abstract

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.

DOI
10.1364/josab.31.000656

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We investigate the efficiency of inseparability criteria in detecting the entanglement properties of two-mode non-Gaussian states of the electromagnetic field. We focus our study on the relevant class of two-mode squeezed number states. These states combine the entangling capability of two-mode squeezers with the non-Gaussian character (nonclassicality) of number states. They allow for some exact analytical treatments, and include as a particular case the two-mode Gaussian squeezed vacuum. We show that the generalized PPT criterion recently proposed by Shchukin and Vogel, based on higher order statistical moments, is very efficient in detecting the entanglement for this class of non-Gaussian states.
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In this Letter, we show that the fulfillment of uncertainty relations is a sufficient criterion for a quantum-mechanically permissible state. We specifically construct two pseudospin observables for an arbitrary nonpositive Hermitian matrix whose uncertainty relation is violated. This method enables us to systematically derive separability conditions for all negative partial-transpose states in experimentally accessible forms. In particular, generalized entanglement criteria are derived from the Schrödinger-Robertson inequalities for bipartite continuous-variable states.
We formulate an entanglement criterion using Peres-Horodecki positive partial transpose operations combined with the Schr\"odinger-Robertson uncertainty relation. We show that any pure entangled bipartite and tripartite state can be detected by experimentally measuring mean values and variances of specific observables. Those observables must satisfy a specific condition in order to be used, and we show their general form in the $2\ifmmode\times\else\texttimes\fi{}2$ (two qubits) dimension case. The criterion is applied on a variety of physical systems including bipartite and multipartite mixed states and reveals itself to be stronger than the Bell inequalities and other criteria. The criterion also work on continuous variable cat states and angular momentum states of the radiation field.