Abstract
We consider universal methods for obtaining (uniform) continuity bounds for characteristics of multipartite quantum systems. We pay special attention to infinite-dimensional multipartite quantum systems under the energy constraints. By these methods, we obtain continuity bounds for several important characteristics of a multipartite quantum state: the quantum (conditional) mutual information, the squashed entanglement, the c-squashed entanglement, and the conditional entanglement of mutual information. The continuity bounds for the multipartite quantum mutual information are asymptotically tight for large dimension/energy. The obtained results are used to prove the asymptotic continuity of the n-partite squashed entanglement, the c-squashed entanglement, and the conditional entanglement of mutual information under the energy constraints.
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