Experimental criteria for steering and the Einstein-Podolsky-Rosen paradox

Abstract

We formally link the concept of steering (a concept created by Schrödinger but only recently formalized by Wiseman, Jones, and Doherty ͓Phys. Rev. Lett. 98, 140402 ͑2007͔͒) and the criteria for demonstrations of Einstein-Podolsky-Rosen ͑EPR͒ paradox introduced by Reid ͓Phys. Rev. A 40, 913 ͑1989͔͒. We develop a general theory of experimental EPR-steering criteria, derive a number of criteria applicable to discrete as well as continuous-variable observables, and study their efficacy in detecting that form of nonlocality in some classes of quantum states. We show that previous versions of EPR-type criteria can be rederived within this formalism, thus unifying these efforts from a modern quantum-information perspective and clarifying their conceptual and formal origin. The theory follows in close analogy with criteria for other forms of quantum nonlocality ͑Bell nonlocality and entanglement͒, and because it is a hybrid of those two, it may lead to insights into the relationship between the different forms of nonlocality and the criteria that are able to detect them.

Quantum steering of multimode Gaussian states by Gaussian measurements: monogamy relations and the Peres conjecture

“…The inferred variance ofB i with its estimate B i,est (A i ) based on the outcome A i is defined by [28,29] …”

Violation of Continuous-Variable Einstein-Podolsky-Rosen Steering with Discrete Measurements

“…This occurs when the conditional or inferred measurement outcomes of B no longer obey the same uncertainty relations that a single particle does [13]. In such a case, we demonstrate EPR's dichotomy, that either quantum mechanics offers an incomplete description of B, or we must allow that these correlations can be nonlocal in nature.…”

Non-Gaussian continuous-variable entanglement and steering

“…As shown by Wiseman et al [31] and Cavalcanti et al [32], the inseparability of the system density matrix describes a set of states which includes, within it, subsets which are more deeply nonclassical than evidenced by entanglement alone, such as those which demonstrate the EPR paradox [33]. For our purposes here, we will use the inequality developed by Reid [34], written as…”