Locally-Measured Rényi Divergences

IEEE International Symposium on Information Theory (ISIT), pp. 351–356

Abstract

We propose an extension of the classical Rényi divergences to quantum states through an optimization over probability distributions induced by restricted sets of measurements. In particular, we define the notion of locally-measured Rényi divergences, where the set of allowed measurements orig-inates from locality constraints between (distant) parties$A$and$B$. As our main result, we derive variational characterizations of these locally-measured Rényi divergences. We then evaluate them for variants of data-hiding states, showcasing the reduced distinguishing power of locality-constrained measurements, and give corresponding applications in locally-measured hypothesis testing.

Authors 3

1. Tobias Rippchen Aachen Institute for Quantum Information

   RWTH Aachen University

   Affiliation as printed

   Institute for Quantum Information, RWTH Aachen University,Aachen,Germany

2. Sreejith Sreekumar Aachen Institute for Quantum Information

   RWTH Aachen University

   Affiliation as printed

   Institute for Quantum Information, RWTH Aachen University,Aachen,Germany

3. Mario Berta Aachen Institute for Quantum Information

   RWTH Aachen University

   Affiliation as printed

   Institute for Quantum Information, RWTH Aachen University,Aachen,Germany