Exact Quantum Correlations of Conjugate Variables From Joint Quadrature Measurements

TL;DR

This paper shows that joint quadrature measurements can precisely determine quantum correlations of conjugate variables, revealing new insights into phase space probabilities beyond traditional position and momentum distributions.

Contribution

It introduces a method to exactly measure quantum correlations of conjugate variables using joint quadrature measurements, highlighting their significance in quantum phase space analysis.

Findings

Exact measurement of correlations using joint quadrature measurements

Phase space probabilities must be modified to include correlations

Demonstrates differences in phase space for EPR and coherent states

Abstract

We demonstrate that for two canonically conjugate operators $\hat{q},\hat {p} $,the global correlation $\langle \hat{q} \hat {p} + \hat{p} \hat {q} \rangle -2 \langle \hat{q}\rangle \langle \hat {p}\rangle$, and the local correlations $\langle \hat{q} \rangle (p) - \langle \hat{q}\rangle$ and $\langle \hat{p} \rangle (q)-\langle \hat {p}\rangle$ can be measured exactly by Von Neumann-Arthurs-Kelly joint quadrature measurements . These correlations provide a sensitive experimental test of quantum phase space probabilities quite distinct from the probability densities of $ q,p $. E.g. for EPR states, and entangled generalized coherent states, phase space probabilities which reproduce the correct position and momentum probability densities have to be modified to reproduce these correlations as well.