Detecting Entanglement Between Modes of Light

TL;DR

This paper investigates how certain optical setups can be used to detect quantum entanglement by violating Bell inequalities, focusing on the role of interferometers and photon-number detectors.

Contribution

It introduces a method to demonstrate entanglement between light modes using a specific subgroup of unitary transformations and photon-number detection, highlighting optimal local settings.

Findings

Maximal violation of CHSH inequality identified

Uncertainty principles between observables established

Optical configurations for entanglement detection characterized

Abstract

We consider a subgroup of unitary transformations on a mode of light induced by a Mach-Zehnder Interferometer and an algebra of observables describing a photon-number detector proceeded by an interferometer. We explore the uncertainty principles between such observables and their usefulness in performing a Bell-like experiment to show a violation of the CHSH inequality, under physical assumption that the detector distinguishes only zero from non-zero number of photons. We show which local settings of the interferometers lead to a maximal violation of the CHSH inequality.