Optimal Discrimination of Qubit States - Methods, Solutions, and Properties

Abstract

We show a geometric formulation for minimum-error discrimination of qubit states, that can be applied to arbitrary sets of qubit states given with arbitrary a priori probabilities. In particular, when qubit states are given with equal \emph{a priori} probabilities, we provide a systematic way of finding optimal discrimination and the complete solution in a closed form. This generally gives a bound to cases when prior probabilities are unequal. Then, it is shown that the guessing probability does not depend on detailed relations among given states, such as angles between them, but on a property that can be assigned by the set of given states itself. This also shows how a set of quantum states can be modified such that the guessing probability remains the same. Optimal measurements are also characterized accordingly, and a general method of finding them is provided.

5 pages, 1 figure

References in corpus (3)

• Experimental Quantum State Tomography of Optical Fields and Ultrafast Statistical Sampling
• Unknown Quantum States and Operations, a Bayesian View
• Qubit State Discrimination

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• Contextual advantages and certification for maximum confidence discrimination
• Complete analysis for three-qubit mixed-state discrimination
• Optimal measurements for the discrimination of quantum states with a fixed rate of inconclusive results
• Optimal discrimination of single-qubit mixed states
• An optimal discrimination of two mixed qubit states with a fixed rate of inconclusive results
• Maximum confidence measurement for qubit states
• Preserving Measurements for Optimal State Discrimination over Quantum Channels
• Multiple-copy state discrimination of noisy qubits
• Multi-state and multi-hypothesis discrimination with open quantum systems
• A Structure of Minimum Error Discrimination for Linearly Independent States
• Distinguishability, Ensemble Steering, and the No-Signaling Principle
• Quantum State Discrimination Circuits Inspired by Deutschian Closed Timelike Curves
• A simple relation of guessing probability in quantum key distribution
• Violating the Modified Helstrom Bound with Nonprojective Measurements
• Protocol for nonlinear state discrimination in rotating condensate
• Quantum process discrimination with restricted strategies
• Qubit State Discrimination using Post-measurement Information
• Minimum-error discrimination of thermal states
• Complete analysis to minimum-error discrimination of mixed four qubit states with arbitrary prior probabilities