Estimating optical frequency difference using optimized coherent detection

Recent results in quantum parameter estimation using optical signals have shown that long accepted precision limits (like the Rayleigh criterion) are just an artifact of using a suboptimal measurement. In many tasks, the quantum Fisher information is larger than the Fisher information associated with traditional receivers, such as direct detection. Depending on the parameter to be estimated, implementing the optimal measurement may be experimentally demanding. However, simpler measurements, though suboptimal, could still be superior to the traditional detection strategies. To that end, we theoretically and experimentally investigate the quantum limit for two tasks of interest when we are measuring the spectral properties of two similar photon-starved optical signals with overlapping spectra. First, we compute the classical and quantum Chernoff bound for discriminating between the two states. Second, we analyze a modified coherent detection scheme to estimate the frequency separation between the two signals when they are incoherently combined, optimizing the spectral shape of the local oscillator to improve the estimation precision of the measurement.