Exact Quantum Correlations of Conjugate Variables From Joint Quadrature Measurements

Abstract

We demonstrate that for two canonically conjugate operators $\hat{q},\hat{p}$,the global correlation $⟨\hat{q}\hat{p}+\hat{p}\hat{q}⟩-2⟨\hat{q}⟩⟨\hat{p}⟩$, and the local correlations $⟨\hat{q}⟩(p)-⟨\hat{q}⟩$ and $⟨\hat{p}⟩(q)-⟨\hat{p}⟩$ 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.

5 pages, 1 figure

References in corpus (3)

• Heisenberg's Uncertainty Principle
• Classical Representations of Quantum Mechanics Related to Statistically Complete Observables
• Practical schemes for the measurement of angular-momentum covariance matrices in quantum optics

Cited by in corpus (3)

• Remote Tomography Via von Neumann-Arthurs-Kelly Interaction
• Optimum Phase Space Probabilities From Quantum Tomography
• Symplectic group methods and the Arthurs Kelly model of measurement in quantum mechanics