  Mutual information is the reciprocal information that is common to or shared
by two or more parties. Quantum mutual information for bipartite quantum
systems is non-negative, and bears the interpretation of total correlation
between the two subsystems. This may, however, no longer be true for three or
more party quantum systems. In this paper, we propose an alternative definition
of multipartite information taking into account the shared information between
two and more parties. It is non-negative, observes monotonicity under partial
trace as well as completely positive maps, and equals multipartite information
measure in literature for pure states. We then define multiparty quantum
discord, and give some examples. Interestingly, we observe that quantum discord
increases when measurement is performed on a large number of subsystems.
Consequently, the symmetric quantum discord, which involves measurement on all
parties, reveals the maximal quantumness. This raises question on the
interpretation of measured mutual information as classical correlation.
