Distributed Quantum Hypothesis Testing under Zero-rate Communication Constraints

• URL: http://arxiv.org/abs/2410.08937v1
• Date: Fri, 11 Oct 2024 16:03:10 GMT
• Title: Distributed Quantum Hypothesis Testing under Zero-rate Communication Constraints
• Authors: Sreejith Sreekumar, Christoph Hirche, Hao-Chung Cheng, Mario Berta,
• Abstract summary: We study a distributed binary hypothesis testing problem to infer a bipartite quantum state shared between two remote parties. As our main contribution, we derive an efficiently computable single-letter formula for the Stein's exponent of this problem. As a key tool for proving the converse direction of our results, we develop a quantum version of the blowing-up lemma.
• Score: 14.29947046463964
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 classical information to the tester at zero-rate (while the other party communicates classical or quantum information 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. For the general case, we show that the Stein's exponent is given by a multi-letter expression involving max-min optimization of regularized measured relative entropy. While this becomes single-letter for the fully classical case, we further prove that this already does not happen in the same way for classical-quantum states in general. 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.

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