Wigner functions and statistical moments of quantum states with definite parity

A M Ozorio de Almeida, Olivier Brodier

Notwithstanding radical conceptual differences between classical and quantum mechanics, it is usually assumed that physical measurements concern observables common to both theories. Not so with the eigenvalues (±1) of the parity operator. The effect of such a measurement on a mixture of even and odd states of the harmonic oscillator is akin to separating at a single stroke a pair of shuffled card decks: the result is a set of definite parity, though otherwise mixed. Here we derive the general form of a parity collapsed state, whether pure or mixed. The signature of positive or negative parity is a corresponding spike in the Wigner function which is sharpened by decoherence. We conjecture that states with pure parity always have negative values in their Wigner functions.

A V Gorbachev

Hui Li

Konrad Banaszek, Krzysztof Wódkiewicz

We demonstrate that the Wigner function of the Einstein-Podolsky-Rosen state, though positive definite, provides direct evidence of the nonlocal character of this state. The proof is based on an observation that the Wigner function describes correlations in the joint measurement of the phase-space displaced parity operator.

Konrad Banaszek, Czesław Radzewicz, K. Wódkiewicz +1 more

We present an experimental realisation of the direct scheme for measuring the Wigner function of a single quantized light mode. In this method, the Wigner function is determined as the expectation value of the photon number parity operator for the phase space displaced quantum state.

Antoine Royer