an alternative generalization of mutual information to the quantum case. The difference between the two for a given state is called quantum discord, a measure for the quantum correlations of the state in question. Properties When the state is pure (and thus , the mutual information is twice the entanglement entropy of the state: A positive quantum mutual information is not necessarily indicative of entanglement, however. A classical mixture of separable states will always have zero entanglement, but can have nonzero QMI, such as In this case, the state is merely a classically correlated state. Multiparty generalization Suppose a system is composed by n subsystems then: where and the sum is over all the distinct combinations of the subsystem without repetition. For example, take : Take now : Note that what we are actually doing is taking the partial trace over one subsystem per time, take the example, in the first term we are tracing over , in the second term the trace is over and so on. References Quantum mechanical entropy Quantum information theory