Distinguishing between Nonorthogonal Quantum States of a Single Nuclear Spin

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