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Demonstrations of quantum advantage have largely focused on computationalspeedups and on quantum simulation of many-body physics, limited by fidelityand capability of current devices. Discriminating laser-pulse-modulatedclassical-communication codewords at the minimum allowable probability of errorusing universal-quantum processing presents a promising parallel direction, onethat is of both fundamental importance in quantum state discrimination, as wellas of technological relevance in deep-space laser communications. Here wepresent an experimental realization of a quantum joint detection receiver forbinary phase shift keying modulated codewords of a 3-bit linear tree code usinga recently-proposed quantum algorithm: belief propagation with quantummessages. The receiver, translated to a quantum circuit, was experimentallyimplemented on a trapped-ion device -- the recently released Honeywell LT-1.0system using ${}^{171}Yb+ $ ions, which possesses all-to-all connectivity andmid-circuit measurement capabilities that are essential to this demonstration.We conclusively realize a previously postulated but hitherto not-demonstratedjoint quantum detection scheme, and provide an experimental framework thatsurpasses the quantum limit on the minimum average decoding error probabilityassociated with pulse-by-pulse detection in the low mean photon number limit.The full joint-detection scheme bridges across photonic and trapped-ion basedquantum information science, mapping the photonic coherent states of themodulation alphabet onto inner product-preserving states of single-ion qubits.Looking ahead, our work opens new avenues in hybrid realizations ofquantum-enhanced receivers with applications in astronomy and emergingspace-based platforms.

Demonstration of quantum advantage by a joint detection receiver for optical communications using quantum belief propagation on a trapped-ion device