Quantum Sequential Hypothesis Testing

Abstract

We introduce sequential analysis in quantum information processing, by focusing on the fundamental task of quantum hypothesis testing. In particular our goal is to discriminate between two arbitrary quantum states with a prescribed error threshold, $\epsilon$, when copies of the states can be required on demand. We obtain ultimate lower bounds on the average number of copies needed to accomplish the task. We give a block-sampling strategy that allows to achieve the lower bound for some classes of states. The bound is optimal in both the symmetric as well as the asymmetric setting in the sense that it requires the least mean number of copies out of all other procedures, including the ones that fix the number of copies ahead of time. For qubit states we derive explicit expressions for the minimum average number of copies and show that a sequential strategy based on fixed local measurements outperforms the best collective measurement on a predetermined number of copies. Whereas for general states the number of copies increases as $\log 1/\epsilon$, for pure states sequential strategies require a finite average number of samples even in the case of perfect discrimination, i.e., $\epsilon =0$.

arXiv comment17 pages, 8 figures

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• Optimized mitigation of random-telegraph-noise dephasing by spectator-qubit sensing and control
• Quantum Receiver Enhanced by Adaptive Learning
• Ultimate limits for quickest quantum change-point detection
• Certifying the Topology of Quantum Networks: Theory and Experiment
• Optimal Adaptive Strategies for Sequential Quantum Hypothesis Testing
• Parallelization of Adaptive Quantum Channel Discrimination in the Non-Asymptotic Regime
• Experimental Test of Nonlocality Limits from Relativistic Independence
• Identification of malfunctioning quantum devices
• Experimental Realization of Genuine Three-copy Collective Measurements for Optimal Information Extraction
• Sequential hypothesis testing for continuously-monitored quantum systems
• Universal algorithms for quantum data learning
• Generalising the Horodecki criterion to nonprojective qubit measurements
• Mermin and Svetlichny inequalities for non-projective measurement observables
• Fundamental Limits Of Quickest Change-point Detection With Continuous-Variable Quantum States
• Quantum hypothesis testing via robust quantum control
• Bounds in Sequential Unambiguous Discrimination of Multiple Pure Quantum States
• Optimal estimation of three parallel spins with genuine and restricted collective measurements
• Online identification of symmetric pure states