Uniform continuity bounds for characteristics of multipartite quantum systems

Abstract

We consider universal methods for obtaining (uniform) continuity bounds for characteristics of multipartite quantum systems. We pay a 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, c-squashed entanglement and the conditional entanglement of mutual information under the energy constraints.

30 pages, v.2 is an improved version, any comments are welcome

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Cited by in corpus (6)

• Asymptotic state transformations of continuous variable resources
• From Classical to Quantum: Uniform Continuity Bounds on Entropies in Infinite Dimensions
• Continuity of characteristics of composite quantum systems
• Attainability and lower semi-continuity of the relative entropy of entanglement, and variations on the theme
• Multipartite Intrinsic Non-Locality and Device-Independent Conference Key Agreement
• Close-to-optimal continuity bound for the von Neumann entropy and other quasi-classical applications of the Alicki-Fannes-Winter technique