Simplified Quantum Optical Stokes observables and Bell's Theorem

TL;DR

This paper introduces a simplified, binning-based form of quantum optical Stokes observables that can be used in Bell tests, especially with states of undefined photon number like squeezed vacuum, leading to robust Bell inequality violations.

Contribution

It proposes a new simplified Stokes observable based on binning that is practical for Bell tests with quantum optical fields of undefined photon number.

Findings

Enables Bell tests with simplified observables

Achieves robust Bell inequality violations with squeezed vacuum

Applicable to states with undefined photon number

Abstract

We introduce a simplified form of Stokes operators for quantum optical fields that involve the known concept of binning. Behind polarization analyzer photon numbers (more generally intensities) are measured. If the value obtained in one of the outputs, say H, is greater the than in the other one, V, then the value of the simplified Stokes operator is, say, 1, otherwise it is -1. For equal photon numbers we put 0. Such observables do not have all properties of the Stokes operators, but surprisingly can be employed in Bell type measurements, involving polarization analyzers. They are especially handy for states of undefined number of photons, e.g. squeezed vacuum. We show that surprisingly they can lead to quite robust violations of associated Bell inequalities.