Understanding the fundamental sensitivity limit of an optical sensor requires a full quantum mechanical description of the sensing task. In this work, we calculate the fundamental (quantum) limit for discriminating between pure laser light and thermal noise in a photon-starved regime. The Helstrom bound for discrimination error probability for single mode measurement is computed along with error probability bounds for direct detection, coherent homodyne detection and the Kennedy receiver. A generalized Kennedy (GK) receiver is shown to closely approach the Helstrom limit. We present an experimental demonstration of this sensing task and demonstrate a 15.4 dB improvement in discrimination sensitivity over direct detection using a GK receiver and an improvement of 19.4% in error probability over coherent detection.

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Models of front propagation like the famous FKPP equation have extensive applications across scientific disciplines e.g., in the spread of infectious diseases. A common feature of such models is the existence of a static state into which to propagate, e.g., the uninfected host population. Here, we instead model an infectious front propagating into a growing host population. The infectious agent spreads via self-similar waves whereas the amplitude of the wave of infected organisms increases exponentially. Depending on the population under consideration, wave speeds are either advanced or retarded compared to the non-growing case. We identify a novel selection mechanism in which the shape of the infectious wave controls the speeds of the various waves and we propose experiments with bacteria and bacterial viruses to test our predictions. Our work reveals the complex interplay between population growth and front propagation.

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