Analysis to optimal unambiguous discrimination of three pure quantum states

Donghun Ha (Hanyang University)

We consider unambiguous discrimination of three linearly independent quantum states. The necessary 
and sufficient conditions are provided to decide which states should be detected for optimal
 measurement of unambiguous discrimination, in terms of inner products and geometric phase ¥Õ. We
 first provide the optimal measurement and probability, in cases where optimal unambiguous
 discrimination is not necessary to detect all quantum states. When at least two quantum states are
 orthogonaltoeachother,wesupplytheoptimalmeasurementandoptimalfailureprobabilityin analytic form.
 When all three quantum states are not orthogonal to each other and ¥Õ=0, we find the analytic
 condition to determine the zero and non-zero elements for an optimal positive operator valued
 measure. We explain how to determine the solution in a geometric manner.