Optimal discrimination of single-qubit mixed states

Abstract

We consider the problem of minimum-error quantum state discrimination for single-qubit mixed states. We present a method which uses the Helstrom conditions constructively and analytically; this algebraic approach is complementary to existing geometric methods, and solves the problem for any number of arbitrary signal states with arbitrary prior probabilities.

arXiv comment8 pages, 1 figure

References in corpus (25)

• Quantum Copying: Beyond the No-Cloning Theorem
• Unambiguous Discrimination Between Linearly-Independent Quantum States
• Quantum state discrimination and its applications
• Phase covariant quantum cloning
• Optimal universal quantum cloning and state estimation
• Optimal Cloning of Pure States, Judging Single Clones
• Maximum Confidence Quantum Measurements
• Dimension witnesses and quantum state discrimination
• Optimal discrimination of mixed quantum states involving inconclusive results
• Accessible information and optimal strategies for real symmetrical quantum sources
• Minimum-error discrimination between three mirror-symmetric states
• Finding optimal strategies for minimum-error quantum-state discrimination
• Structure of minimum-error quantum state discrimination
• Unambiguous Discrimination Between Linearly Dependent States with Multiple Copies
• A Return to the Optimal Detection of Quantum Information
• How continuous quantum measurements in finite dimension are actually discrete
• Optimal Discrimination of Qubit States - Methods, Solutions, and Properties
• A family of generalized `pretty good' measurements and the minimal-error pure-state discrimination problems for which they are optimal
• Measurement does not always aid state discrimination
• Complete analysis for three-qubit mixed-state discrimination
• Qubit State Discrimination
• Minimum error discrimination problem for pure qubit states
• Optimal measurements for the discrimination of quantum states with a fixed rate of inconclusive results
• Optimal quantum state discrimination via nested binary measurements
• Results in Optimal Discrimination

Cited by in corpus (8)

• Locally distinguishing quantum states with limited classical communication
• The Helstrom measurement: A nondestructive implementation
• Multiple-copy state discrimination of noisy qubits
• A Structure of Minimum Error Discrimination for Linearly Independent States
• Quantum State Discrimination on Reconfigurable Noise-Robust Quantum Networks
• Geometric Bloch Vector Solution to Minimum Error Discriminations of Mixed Qubit States
• Quantum State Discrimination Circuits Inspired by Deutschian Closed Timelike Curves
• POVMs are equivalent to projections for perfect state exclusion of three pure states in three dimensions