Optimal Adaptive Strategies for Sequential Quantum Hypothesis Testing

Abstract

We consider sequential hypothesis testing between two quantum states using adaptive and non-adaptive strategies. In this setting, samples of an unknown state are requested sequentially and a decision to either continue or to accept one of the two hypotheses is made after each test. Under the constraint that the number of samples is bounded, either in expectation or with high probability, we exhibit adaptive strategies that minimize both types of misidentification errors. Namely, we show that these errors decrease exponentially (in the stopping time) with decay rates given by the measured relative entropies between the two states. Moreover, if we allow joint measurements on multiple samples, the rates are increased to the respective quantum relative entropies. We also fully characterize the achievable error exponents for non-adaptive strategies and provide numerical evidence showing that adaptive measurements are necessary to achieve our bounds under some additional assumptions.

31 pages, 4 figures

References in corpus (5)

• The Quantum Chernoff Bound
• The Chernoff lower bound for symmetric quantum hypothesis testing
• Error Exponent in Asymmetric Quantum Hypothesis Testing and Its Application to Classical-Quantum Channel coding
• The Converse Part of The Theorem for Quantum Hoeffding Bound
• Quantum Sequential Hypothesis Testing

Cited by in corpus (5)

• Ultimate limits for quickest quantum change-point detection
• Parallelization of Adaptive Quantum Channel Discrimination in the Non-Asymptotic Regime
• Sequential hypothesis testing for continuously-monitored quantum systems
• Optimisation of time-ordered processes in the finite and asymptotic regime
• Bounds in Sequential Unambiguous Discrimination of Multiple Pure Quantum States