Experimental quantum channel discrimination using metastable states of a trapped ion

We present experimental demonstrations of accurate and unambiguous single-shot discrimination between three quantum channels using a single trapped ${}^{40}{\text{Ca}}^{+}$ ion. The three channels cannot be distinguished unambiguously using repeated single channel queries, the natural classical analogue. We develop techniques for using the 6-dimensional ${\text{D}}_{5\mathrm{/}2}$ state space for quantum information processing, and we implement protocols to discriminate quantum channel analogues of phase shift keying and amplitude shift keying data encodings used in classical radio communication. The demonstrations achieve discrimination accuracy exceeding $99\mathrm{\%}$ in each case, limited entirely by known experimental imperfections.