  It was recently shown by Hansen that the Wigner-Yanase entropy is, for
general states of quantum systems, not subadditive with respect to
decomposition into two subsystems, although this property is known to hold for
pure states. We investigate the question whether the weaker property of
subadditivity for pure states with respect to decomposition into more than two
subsystems holds. This property would have interesting applications in quantum
chemistry. We show, however, that it does not hold in general, and provide a
counterexample.
