QIP2021 | New quantum Rényi divergences and their application to device-independent... (Peter Brown)

New quantum Rényi divergences and their application to device-independent cryptography and quantum Shannon theory

Authors: Peter Brown, Hamza Fawzi and Omar Fawzi
Affiliations: ENS Lyon | University of Cambridge | ENS Lyon

Abstract:
In the analysis of quantum information processing tasks, the choice of distance measure between states or channels often plays a crucial role. This submission introduces new quantum Rnyi divergences for states and channels that are based on a convex optimization program involving the matrix geometric mean. These divergences have mathematical and computational properties that make them applicable to a wide variety of problems. We use these Rnyi divergences to obtain semidefinite programming lower bounds on the key rates for device-independent cryptography, and in particular we find a new bound on the minimal detection efficiency required to perform device-independent quantum key distribution without additional noisy preprocessing. Furthermore, we give several applications to quantum Shannon theory, in particular proving that adaptive strategies do not help in the strong converse regime for quantum channel discrimination and obtaining improved bounds for quantum capacities.

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