1305.0410 (S. M. Roy)

Exact Quantum Correlations of Conjugate Variables From Joint Quadrature
Measurements    [PDF]

S. M. Roy

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.

View original: http://arxiv.org/abs/1305.0410