Multipartite Quantum Correlation and Communication Complexities

The concepts of quantum correlation complexity and quantum communication complexity were recently proposed to quantify the minimum amount of resources needed in generating bipartite classical or quantum states in the single-shot setting. The former is the minimum size of the initially shared state $${\sigma}$$ on which local operations by the two parties (without communication) can generate the target state $${\rho}$$ , and the latter is the minimum amount of communication needed when initially sharing nothing. In this paper, we generalize these two concepts to multipartite cases, for both exact and approximate state generation. Our results are summarized as follows.