Experimental quantum channel discrimination using metastable states of a trapped ion

One of the hallmarks of quantum mechanics is the impossibility of perfectly distinguishing non-orthogonal states. Extending this to the task of discriminating among quantum channels (e.g. unitaries or measurements) reveals a richer problem, where seemingly non-orthogonal channels can sometimes be distinguished with certainty. Using quantum signal processing-based algorithms, we present experimental demonstrations of accurate and unambiguous single-shot discrimination between three quantum channels using a single trapped 40Ca+ ion. These channels cannot be distinguished unambiguously using repeated single-use queries, the natural classical analogue, which have at most a 2/3 probability of successful identification. However, coherently interleaving the channel queries with quantum signal processing operations enables us to design response functions to extract information about the channel. We develop techniques for using the 6-dimensional D5/2 state space for this task, implementing protocols to discriminate among the quantum channel analogues of two data encodings commonly used in classical radio communication. These demonstrations achieve discrimination accuracy exceeding 99%, with inaccuracy entirely attributable to known experimental imperfections.