# Experimental Realization of Optimal Quantum Measurements

Due to imperfections, real measurements on quantum systems are seldom ideal projective measurements. Moreover, it is sometimes advantageous to deliberately design a quantum measurement that is not projective, depending on exactly what property of the measured quantum system one is interested in. One example is when distinguishing between non-orthogonal quantum states. This is not possible to achieve perfectly with certainty, but can be optimized with respect to two aspects: One the one hand, the probability the get a correct result can be maximized, which is the so called Helstrom measurement. On the other hand, the measurement can be unambiguous, such that each result is correct, at the expense of having inconclusive results. This is the so called Ivanovic-Dieks-Peres (IDP) measurement. This type of measurement is relevant for important quantum information tasks in quantum cryptography and in entanglement swapping protocols. Moreover, it can be useful for quantum communication, when the two signal states are non-orthogonal after passing through a channel.

Here, we present and compare experimental realizations of optimal quantum measurements for distinguishing between two non-orthogonal quantum states encoded in a single nuclear spin associated with the nitrogen vacancy defect in diamond. This is the first solid state based implementation of this type of measurement. The figures show the pulse sequence for the IDP measurement, and the probability to obtain a correct result, in dependence of the overlap of the two non-orthogonal states, for the Helstrom, IDP, and standard non optimal measurement.