Asymmetric Gaussian steering: When Alice and Bob disagree

Abstract

Asymmetric steering is an effect whereby an inseparable bipartite system can be found to be described by either quantum mechanics or local hidden variable theories depending on which one of Alice or Bob makes the required measurements. We show that, even with an inseparable bipartite system, situations can arise where Gaussian measurements on one half are not sufficient to answer the fundamental question of which theory gives an adequate description and the whole system must be considered. This phenomenon is possible because of an asymmetry in the definition of the original Einstein-Podolsky-Rosen paradox and in this article we show theoretically that it may be demonstrated, at least in the case where Alice and Bob can only make Gaussian measurements, using the intracavity nonlinear coupler.

Improved quantum correlations in second harmonic generation with a squeezed pump

“…For the present system, this allows us to consider continuous-variable bipartite entanglement [10,11] and demonstra- tions of the Einstein-Podolsky-Rosen paradox [14], more recently labelled steering [26]. Asymmetric Gaussian steering has previously been theoretically analysed using an unbalanced nonlinear coupler [27] and experimentally produced using parametric downconversion [28]. The phenomenon of entanglement between the fundamental and harmonic fields has been predicted [9] and subsequently labelled harmonic entanglement [12].…”

On Schmidt Decomposition: Approach Based on Correlation Operator as Bipartite Entanglement Entity

“…For example, steering was generalized to mixed states in [27]. Asymmetric steering was studied in [28]. See also the review article in [29].…”

Non-Gaussian continuous-variable entanglement and steering

“…Although entangled states have already been predicted to be produced by the intracavity nonlinear coupler [26,27], the linearization process used to obtain the spectra in those cases forces Gaussian statistics on the outputs. Here, we wish to produce entangled states that maintain non-Gaussian statistics, so we will proceed by mixing the outputs of two Kerr oscillators on a beam splitter [28] as experimentally demonstrated by Ref.…”