Quantum-enhanced measurements can provide information about the properties of a physical system with sensitivities beyond what is fundamentally possible with conventional technologies. However, this advantage can be achieved only if quantum measurement technologies are robust against losses and real-world imperfections, and can operate in regimes compatible with existing systems. Here, we demonstrate a quantum receiver for coherent communication, the performance of which not only surpasses the standard quantum limit, but does so for input powers extending to high mean photon numbers. This receiver uses adaptive measurements and photon number resolution to achieve high sensitivity and robustness against imperfections, and ultimately shows the greatest advantage over the standard quantum limit ever achieved by any quantum receiver at power levels compatible with state-of-the-art optical communication systems. Our demonstration shows that quantum measurements can provide real and practical advantages over conventional technologies for optical communications.M easurements based on the quantum properties of physical systems have revolutionized our understanding of information and have enabled many tasks that are not possible by any classical means. Measurements taking advantage of quantum resources have given birth to quantum communication 1,2 and quantum metrology 3,4 , which are crucial for many quantum technologies, including quantum computing 5,6 , with potential capabilities far beyond the limits of their classical counterparts. Quantum measurements for the discrimination of non-orthogonal coherent states, which cannot be perfectly discriminated due to their inherent quantum noise 7 , can enable discrimination below the standard quantum limit (SQL) 8-10 and approach the ultimate limit allowed by quantum mechanics. These measurements have great potential for improving communication technologies and many quantum information applications.Coherent states are excellent carriers of quantum and classical information due to their intrinsic resilience to loss and their highspectral-efficiency capabilities. Optical communications based on coherent states can now reach terabit-per-second transmission rates 11,12 . However, the growing need for even higher data transmission rates for communications, cloud computing and other virtualization applications 13 has motivated extensive research into novel multilevel modulation and multiplexing communication formats 14,15 , and low-noise signal amplification 16,17 and processing 18 protocols to further improve spectral efficiency and overall information exchange fidelity. State-of-the-art optical coherent receivers for non-orthogonal coherent states employ direct coherent homodyne or heterodyne detection and are now approaching their ultimate sensitivity limit 19,20 , the SQL. However, quantum mechanics allows for a much lower error bound for non-orthogonal state discrimination-the Helstrom bound 7 . For example, the SQL is about 10 6 times higher than the error rate given by the He...

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We investigate a strategy for M-ary discrimination of nonorthogonal phase states with error rates below the homodyne limit. This strategy uses feed forward to update a reference field and signal nulling for the state discrimination. We experimentally analyze the receiver performance using postprocessing and a Bayesian strategy to emulate the feed-forward process. This analysis shows that for a moderate system detection efficiency, it is possible to surpass the homodyne error limit for quadrature phase-shift keying signals using feed forward.