Loss-tolerant tests of Einstein-Podolsky-Rosen steering

Abstract

We analyse two classes of Einstein-Podolsky-Rosen (EPR)-steering inequalities, the violation of which can be used to demonstrate EPR-steering with an entangled two-qubit Werner state: linear inequalities and quadratic inequalities. We discuss how post-selection of results (by appeal to the fair sampling assumption) can compromise the rigour of these inequalities in experimental tests of EPR-steering. By considering the worst-case scenarios in which detector inefficiency or other loss could be exploited within a local hidden-state model, we derive inequalities that enable rigorous but loss-tolerant demonstrations of EPR-steering. The linear inequalities, and special cases of the quadratic inequalities, have been used in recent experiments. Our results indicate that regardless of the number of settings used, quadratic inequalities are never better, and often worse, than linear inequalities.

Demonstration of Einstein–Podolsky–Rosen steering with enhanced subchannel discrimination

“…SD task for the multi-setting cases. EPR steering from Alice to Bob relates to the number of settings measured by Alice [4,49]. For some predictably steerable states, steering fails because of the very limited number of measurement settings [25].…”

“…In this work, we consider the regularly spaced directions which are given by the Platonic solids with the number of measurement settings n corresponding to 2, 3, 4, 6 and 10 [20]. Compared with the optimal measurement settings introduced in [49], here, the two-and three-setting measurements are optimal and EPR steering can be affirmed necessarily and sufficiently. For other multi-setting cases, the optimal measurements don't correspond to the regularly spaced directions and are difficult to realize in experiment.…”

Optimal measurements for tests of Einstein-Podolsky-Rosen steering with no detection loophole using two-qubit Werner states

“…[15], with more details in Ref. [21]. The analysis in the remainder of the present paper builds on this, so we briefly review it here.…”

“…Reference [21] describes the formulation of these criteria in more detail, also showing them to be more loss-tolerant than another class of EPR-steering criteria (which includes those used in Refs. [19,20]).…”

Some applications of uncertainty relations in quantum information

“…24 where it has been proposed that it may be easier to detect entaglement in some such states using steering compared to the manifestation of Bell violation. Note also that further generalizations of entropic steering inequalities to the case of symmetric steering 53 , loss-tolerant steering 54 , as well as to the case of steering with qauntum memories 55 have also been proposed recently.…”