  Contractive states for a free quantum particle were introduced by Yuen [Yuen
H P 1983 Phys. Rev. Lett. 51, 719] in an attempt to evade the standard quantum
limit for repeated position measurements. We show how appropriate families of
two- and three component ``Schroedinger cat states'' are able to support
non-trivial correlations between the position and momentum observables leading
to contractive behavior. The existence of contractive Schroedinger cat states
is suggestive of potential novel roles of non-classical states for precision
measurement schemes.
