  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 ($\pm 1$) 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. The Wigner function should be a sensitive probe for this phenomenon, for
it can be interpreted as the expectation value of the parity operator. We here
derive the general form of Wigner functions $W_{\pm}$, resulting from an ideal
parity measurement on $W(\x)$. Even if $W(\x)$ resembles a classical
distribution, $W_{\pm}$ displays a quantum spike, which is positive for $W_+$
and negative for $W_-$. However we conjecture that $W_+$ always has negative
values.
