# Quantum-Message-Passing Receiver for Quantum-Enhanced Classical Communications

Error-correcting codes can be used to transmit information in space-based laser communications such that the rate of communication is at the capacity of the underlying quantum channel. However, this requires building a receiver that jointly detects many transmitted pulses together. Since this is much harder to design, usually one implements a receiver that detects one modulated pulse at a time. This is suboptimal. In fact, when the average photon number per pulse is small, which is a realistic regime in this application, there is a large gap between the number of bits that can be reliably communicated per pulse with the joint-detection receiver and the suboptimal one. In this work (https://arxiv.org/abs/2003.04356), in a collaboration between Duke University and University of Arizona at Tucson, Narayanan Rengaswamy, Kaushik P. Seshadreesan, Saikat Guha, and Henry D. Pfister propose a structured receiver construction based on the recent idea of belief-propagation (BP) with *quantum* messages (BPQM) by Joseph Renes at ETH, Zurich (https://arxiv.org/abs/1607.04833). BP is a well-studied algorithm that passes probabilities as "messages" on a graphical representation of classical error-correcting codes in order to decode over classical channels. However, BPQM makes the messages *qubits* in order to decode over channels like the aforementioned space-based optical communication channel. Although Renes proposed the algorithm, simulation or analysis of it was missing. The above team rigorously analyze the scheme on a simple 5-bit code and reveal the subtleties of the algorithm. The key result is that their proposed receiver achieves the same decoding error rate as the quantum-optimal joint-detection receiver. The analysis is verified by simulations. Hence, if one can build a small, special-purpose, photonic quantum computer that implements this receiver, then this points to a new and exciting application in space-based laser communications.