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