Two Copies of the Einstein-Podolsky-Rosen State of Light Lead to Refutation of EPR Ideas

TL;DR

This paper demonstrates that two copies of the EPR state of light can be used to directly test violations of EPR ideas using simple photon number measurements, leading to a GHZ-type contradiction and robust Bell inequality violations.

Contribution

It introduces a new method to test EPR violations with straightforward photon number observables from two EPR state copies, revealing a GHZ-type contradiction.

Findings

Violations of Bell inequalities are resistant to multipair emissions.

A new geometric chained Bell inequality based on photon number measurements.

Demonstration of a GHZ-type contradiction in EPR reasoning.

Abstract

Bell's theorem applies to the normalizable approximations of the original Einstein-Podolsky-Rosen (EPR) state. The constructions of the proof require measurements difficult to perform, and dichotomic observables. By noticing the fact that the four mode squeezed vacuum state produced in type II down-conversion can be seen both as two copies of approximate EPR states, and also as a kind of polarization supersinglet, we show a straightforward way to test violations of the EPR concepts with direct use of their state. The observables involved are simply photon numbers at outputs of polarizing beam splitters. Suitable chained Bell inequalities are based on the geometric concept of distance. For a few settings they are potentially a new tool for quantum information applications, involving observables of a nondichotomic nature, and thus of higher informational capacity. In the limit of infinitely many settings we get a Greenberger-Horne-Zeilinger-type contradiction: EPR reasoning points to a correlation, while quantum prediction is an anticorrelation. Violations of the inequalities are fully resistant to multipair emissions in Bell experiments using parametric down-conversion sources.