Distributed Quantum Hypothesis Testing Against Product States Under Zero-Rate Communication Constraints

IEEE International Symposium on Information Theory (ISIT), pp. 1–6

Abstract

The trade-offs between error probabilities in quantum hypothesis testing are by now well-understood in the centralized setting, but much less is known for distributed settings. Here, we study a distributed binary hypothesis testing problem to infer a bipartite quantum state shared between two remote parties, where one of these parties communicates to the tester at zero-rate, while the other party communicates to the tester at zero-rate or higher. As our main contribution, we derive an efficiently computable single-letter formula for the Stein's exponent of this problem, when the state under the alternative is product. As a key tool for proving the converse direction of our results, we develop a quantum version of the blowing-up lemma which may be of independent interest.

Authors 3

1. Sreejith Sreekumar

   Centre National de la Recherche Scientifique · Laboratoire des signaux et systèmes

   Affiliation as printed

   L2S, Centralesupélec, CNRS,France

2. Mario Berta Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University,Germany

3. Hao–Chung Cheng

   National Taiwan University

   Affiliation as printed

   National Taiwan University,Taiwan Physics Division, NCTS,Department of Electrical Engineering,Taiwan