Generating entangled Schrodinger cat states using a number state and a beam splitter

TL;DR

This paper demonstrates how passing a photon number state through a beam splitter creates entangled states resembling Schrödinger cat states, which can violate Bell's inequality under specific measurement conditions, despite photon loss challenges.

Contribution

It introduces a method to generate entangled Schrödinger cat states from number states and shows their potential to violate Bell's inequality without fair sampling assumptions.

Findings

Bell's inequality can be violated with these entangled states.

Photon loss affects the violation, requiring low-loss conditions or linear optics mitigation.

Violation is possible without fair sampling assumption if measurements are ordered correctly.

Abstract

Passing a photon number state through a balanced beam splitter will produce an entangled state in which the phases of the two output beams are highly correlated. This entangled state can be viewed as a generalized form of a Schrodinger cat state where there is an equal probability amplitude for all possible phases. We show that Bell's inequality can be violated using this entangled state and two distant measuring devices that consist of a single-photon interferometer with a Kerr medium in one path, a set of single-photon detectors, and postselection based on a homodyne measurement. These entangled states are sensitive to photon loss and a violation of Bell's inequality requires either that the losses are inherently small or that their effects have been minimized using linear optics techniques [M. Micuda et al., Phys. Rev. Lett. 109, 180503 (2012)]. Somewhat surprisingly, the use of the fair sampling assumption is not required for a violation of Bell's inequality despite the use of postselection if the measurements are made in the correct order.