Discrimination of two mixed quantum states with maximum confidence and minimum probability of inconclusive results

Abstract

We study an optimized measurement that discriminates two mixed quantum states with maximum confidence for each conclusive result, thereby keeping the overall probability of inconclusive results as small as possible. When the rank of the detection operators associated with the two different conclusive outcomes does not exceed unity we obtain a general solution. As an application, we consider the discrimination of two mixed qubit states. Moreover, for the case of higher-rank detection operators we give a solution for particular states. The relation of the optimized measurement to other discrimination schemes is also discussed.

7 pages, 1 figure, accepted for publication in Phys. Rev. A

References in corpus (21)

• Quantum State Discrimination
• Unambiguous Discrimination Between Linearly-Independent Quantum States
• Maximum Confidence Quantum Measurements
• Unambiguous discrimination of mixed states
• Optimum unambiguous discrimination of two mixed quantum states
• Optimal discrimination of mixed quantum states involving inconclusive results
• Unambiguous discrimination between quantum mixed states
• Reduction Theorems for Optimal Unambiguous State Discrimination of Density Matrices
• Quantum state filtering and discrimination between sets of Boolean functions
• Optimal unambiguous discrimination between subsets of non-orthogonal quantum states
• Distinguishing mixed quantum states: Minimum-error discrimination versus optimum unambiguous discrimination
• Optimal quantum detectors for unambiguous detection of mixed states
• Minimum-error discrimination between subsets of linearly dependent quantum states
• Optimal unambiguous discrimination of two subspaces as a case in mixed state discrimination
• Measurement does not always aid state discrimination
• Optimum unambiguous discrimination of two mixed states and application to a class of similar states
• Optimal unambiguous filtering of a quantum state: An instance in mixed state discrimination
• No-Signalling Bound on Quantum State Discrimination
• Minimum-error discrimination between a pure and a mixed two-qubit state
• Optimal unambiguous state discrimination of two density matrices: A second class of exact solutions
• Unambiguous discrimination of mixed states: A description based on system-ancilla coupling

Cited by in corpus (12)

• Optimum Unambiguous Discrimination of Linearly Independent Pure States
• Optimal discrimination of quantum states with a fixed rate of inconclusive outcomes
• Optimal state discrimination with a fixed rate of inconclusive results: Analytical solutions and relation to state discrimination with a fixed error rate
• Optimal measurements for the discrimination of quantum states with a fixed rate of inconclusive results
• Optimized maximum-confidence discrimination of N mixed quantum states and application to symmetric states
• Maximum confidence measurement for qubit states
• Postselected quantum hypothesis testing
• Contextuality witness inspired by optimal state discrimination
• Ultimate limits of approximate unambiguous discrimination
• Optimal linear optical discrimination of Bell-like states
• Postselected communication over quantum channels
• Excluding false negative error in certification of quantum channels