Optimum unambiguous discrimination of two mixed states and application to a class of similar states

Abstract

We study the measurement for the unambiguous discrimination of two mixed quantum states that are described by density operators ${\rho }_1$ and ${\rho }_2$ of rank d, the supports of which jointly span a 2d-dimensional Hilbert space. Based on two conditions for the optimum measurement operators, and on a canonical representation for the density operators of the states, two equations are derived that allow the explicit construction of the optimum measurement, provided that the expression for the fidelity of the states has a specific simple form. For this case the problem is mathematically equivalent to distinguishing pairs of pure states, even when the density operators are not diagonal in the canonical representation. The equations are applied to the optimum unambiguous discrimination of two mixed states that are similar states, given by ${\rho }_2=U{\rho }_1{U}^{†}$, and that belong to the class where the unitary operator U can be decomposed into multiple rotations in the d mutually orthogonal two-dimensional subspaces determined by the canonical representation.

8 pages, changes in title and presentation

References in corpus (3)

• Maximum Confidence Quantum Measurements
• Unambiguous discrimination of mixed states
• On the generalization of quantum state comparison

Cited by in corpus (7)

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• Commutator Relations Reveal Solvable Structures in Unambiguous State Discrimination
• Quantum state discrimination