Optimum Unambiguous Discrimination of Linearly Independent Pure States

Abstract

Given $n$ linearly independent pure states and their prior probabilities, we study the problem of optimum unambiguous discrimination of these states. We derive the properties of the optimum solution and the equations that must be satisfied by the optimum measurement strategy which achieves the maximum average success probability, and also give the detailed steps to obtain the optimum solution and the optimum measurement strategy. The general method and results we obtain are also illustrated both numerically and geometrically. We derive a simple analytical formula of the maximum average success probability of unambiguous discrimination for a given set of pure states, and it can be used to simplify the calculation of the optimum solution in some situations. We also obtain the analytical solution of a generalized equal-probability measurement problem using the equations we introduce. Finally, as another application of our result, we study the optimum unambiguous discrimination problem of three linearly independent pure states in details and obtain analytical solutions for some special cases.

20 pages, 4 figures and 1 table

References in corpus (12)

• Maximum Confidence Quantum Measurements
• Unambiguous discrimination of mixed states
• Minimum-error discrimination between mixed quantum states
• Optimal Unambiguous Discrimination of Quantum States
• Optimal bounded-error strategies for projective measurements in non-orthogonal state discrimination
• Two-sided estimates of minimum-error distinguishability of mixed quantum states via generalized Holevo-Curlander bounds
• Optimum unambiguous discrimination of two mixed states and application to a class of similar states
• Discrimination of two mixed quantum states with maximum confidence and minimum probability of inconclusive results
• Optimal unambiguous state discrimination of two density matrices: A second class of exact solutions
• Error rates of Belavkin weighted quantum measurements and a converse to Holevo's asymptotic optimality theorem
• Unambiguous discrimination of mixed states: A description based on system-ancilla coupling
• Discrimination between pure states and mixed states

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