  An important task for quantum information processing is optimal
discrimination between two non-orthogonal quantum states, which until now has
only been realized optically. Here, we present and compare experimental
realizations of optimal quantum measurements for distinguishing between two
non-orthogonal quantum states encoded in a single ^14 N nuclear spin.
Implemented measurement schemes are the minimum-error measurement (known as
Helstrom measurement), unambiguous state discrimination using a standard
projective measurement, and optimal unambiguous state discrimination (known as
IDP measurement), which utilizes a three-dimensional Hilbert space. Measurement
efficiencies are found to be above 80% for all schemes and reach a value of 90%
for the IDP measurement
