  The problem of non-orthogonal state discrimination underlies crucial quantum
information tasks, such as cryptography and computing protocols. Therefore, it
is decisive to find optimal scenarios for discrimination among quantum states.
We experimentally investigate the strategy for the optimal discrimination of
two non-orthogonal states considering a fixed rate of inconclusive outcomes
(FRIO). The main advantage of the FRIO strategy is to interpolate between
unambiguous and minimum error discrimination by solely adjusting the rate of
inconclusive outcomes. We present a versatile experimental scheme that performs
the optimal FRIO measurement for any pair of generated non-orthogonal states
with arbitrary a priori probabilities and for any fixed rate of inconclusive
outcomes. Considering different values of the free parameters in the FRIO
protocol, we implement it upon qubit states encoded in the polarization mode of
single photons generated in the spontaneous parametric down-conversion process.
Moreover, we resort to a newfangled double-path Sagnac interferometer to
perform a three-outcome non-projective measurement required for the
discrimination task, showing excellent agreement with the theoretical
prediction. This experiment provides a practical toolbox for a wide range of
quantum state discrimination strategies using the FRIO scheme, which can
greatly benefit quantum information applications and fundamental studies in
quantum theory.
