Bounds in Sequential Unambiguous Discrimination of Multiple Pure Quantum States

Abstract

Sequential methods for quantum hypothesis testing offer significant advantages over fixed-length approaches, which rely on a predefined number of state copies. Despite their potential, these methods remain underexplored for unambiguous discrimination. In this work, we derive performance bounds for such methods when applied to the discrimination of a set of pure states. The performance is evaluated based on the expected number of copies required. We establish a lower bound applicable to any sequential method and an upper bound on the optimal sequential method. The upper bound is derived using a novel and simple non-adaptive method. Importantly, the gap between these bounds is minimal, scaling logarithmically with the number of distinct states.

References in corpus (11)

• The Quantum Chernoff Bound
• Unambiguous Discrimination Between Linearly-Independent Quantum States
• The Chernoff lower bound for symmetric quantum hypothesis testing
• Fundamental limits of quantum error mitigation
• The quantum Chernoff bound as a measure of distinguishability between density matrices: application to qubit and Gaussian states
• Optimum unambiguous discrimination of two mixed quantum states
• Discriminating quantum states: the multiple Chernoff distance
• Quantum Sequential Hypothesis Testing
• Secrecy content of two-qubit states
• Quantum State Discrimination Using the Minimum Average Number of Copies
• Optimal Adaptive Strategies for Sequential Quantum Hypothesis Testing