Distinguishing between Nonorthogonal Quantum States of a Single Nuclear Spin

TLDR

Optimal discrimination between two nonorthogonal quantum states is a key task in quantum information, previously achieved only optically. We experimentally realize and compare optimal quantum measurements for distinguishing two nonorthogonal states encoded in a single 14N nuclear spin of a nitrogen‑vacancy defect in diamond. We implement Helstrom, standard projective, and Ivanovic‑Dieks‑Peres (IDP) measurements—using a three‑dimensional Hilbert space—to benchmark the IDP scheme against conventional projective measurements. All schemes achieve efficiencies above 80%, with the IDP measurement reaching 90%.

Abstract

An important task for quantum-information processing is optimal discrimination between two nonorthogonal quantum states, which until now has been realized only optically. Here, we present and compare experimental realizations of optimal quantum measurements for distinguishing between two nonorthogonal quantum states encoded in a single $^{14}\mathrm{N}$ nuclear spin at a nitrogen-vacancy defect in diamond. 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 Ivanovic-Dieks-Peres (IDP) measurement], which utilizes a three-dimensional Hilbert space. This allows us to benchmark the IDP measurement against the standard projective measurements. Measurement efficiencies are found to be above 80% for all schemes and reach a value of 90% for the IDP measurement.