IV Quantum Hypothesis Testing

Mario Berta, Fernando G. S. L. Brandão, Gilad Gour +4 more

Masahito Hayashi

Hiroshi Nagaoka

Qing Li, Lingna Wang, Min Jiang +3 more

Previous studies in quantum information have recognized that specific types of noise can encode information in certain applications. However, the role of noise in quantum hypothesis testing, traditionally assumed to undermine performance, has not been thoroughly explored. Our study provides sufficient conditions for general noisy dynamics to surpass noiseless (unitary) dynamics within certain time interval. We then design and experimentally implement a noise-assisted quantum hypothesis testing protocol on ultralow-field nuclear magnetic resonance systems, which demonstrates that the success probability under certain noisy dynamics can indeed surpass the ceiling set by unitary evolution. Moreover, we show that in cases where noise initially hampers performance, strategic application of coherent controls on the system can transform those previously detrimental noises into advantageous ones. Our results, both theoretical and experimental, demonstrates the potential to leveraging noise in quantum hypothesis testing, which pushes the boundaries of quantum hypothesis testing and general quantum information processing. In quantum science, quantum hypothesis testing (QHT) is used to determine the model of a given quantum system, but normally the presence of inherent quantum noise hampers perfect hypothesis testing. The authors theoretically and experimentally explore the potential of leveraging noise in quantum hypothesis testing (QHT) to surpass the success probabilities achievable under noiseless dynamics.

Hao–Chung Cheng, Nilanjana Datta, Nana Liu +3 more

We study the sample complexity of quantum hypothesis testing, wherein the goal is to determine the minimum number of samples needed to reach a desired error probability. We characterize the sample complexity of binary quantum hypothesis testing in the symmetric and asymmetric settings, and we provide bounds on the sample complexity of multiple quantum hypothesis testing. The final part of our paper outlines and reviews how sample complexity of quantum hypothesis testing is relevant to a broad swathe of research areas and can enhance understanding of many fundamental concepts, including quantum algorithms for simulation and search, quantum learning and classification, and foundations of quantum mechanics. As such, we view our paper as an invitation to researchers coming from different communities to study and contribute to the problem of sample complexity of quantum hypothesis testing, and we outline a number of open directions for future research.