Event Date
Title: Quantum Universal Hypothesis Testing
Abstract: Hoeffding’s formulation and solution of universal hypothesis testing (UHT) have inspired a substantial body of work on asymmetric hypothesis testing. UHT addresses the problem of determining whether a sequence of independent and identically distributed samples is generated by a given nominal distribution, while allowing the alternative hypothesis to be any fixed but unknown distribution that differs from the nominal. This generality has made UHT widely applicable across numerous real-world settings.
In this work, we introduce the quantum analog of Hoeffding’s UHT: quantum universal hypothesis testing (QUHT). The task is to decide whether a sequence of quantum systems is described by a specified nominal state, providing a natural framework for problems such as quantum system verification and device certification. Motivated by Hoeffding’s strategy — estimating the empirical distribution and constructing a test statistic — we employ quantum state tomography to reconstruct the unknown state prior to forming our test statistic. By leveraging concentration properties of quantum state tomography, we establish the exponential consistency of the proposed test: the type-II error probability decays exponentially fast, with an exponent governed by the trace distance between the true and nominal states. We further discuss the generalization of this scheme to the two-sample setting, the gap between the classical UHT and its quantum counterpart, and potential approaches to (partially) close this gap.
This is a joint work with Arick Grootveld, Haodong Yang, Venkata Gandikota, and Jason Pollack.
Bio: Biao Chen is the John E. and Patricia A. Breyer Professor of Electrical Engineering at Syracuse University. Throughout his academic career, he has worked on a broad range of research challenges in wireless systems, spanning traditional communication networks, sensor networks, and passive sensing systems that exploit ambient RF signals. On the theoretical front, he has made significant contributions to characterizing the capacity of various multi-user networks and designing their optimal transceivers. On the applied side, his group has developed prototype wireless sensing systems and has been selected as finalists in high-profile competitions, including the DARPA Spectrum Challenge and the DARPA Spectrum Collaboration Challenge.
He is an IEEE Fellow and an NSF CAREER Awardee, and has served as an editor and committee member for numerous journals and conferences. He ventured into quantum information theory in 2022 — around the same time he became an avid runner. He has taught quantum information–related courses and has run the Boston Marathon every year starting in 2024. He is actively working to keep both streaks alive.