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Quantum Sensing of Absorbance and the Beer-Lambert Law

Optical quantum sensing strategies that utilise features of quantum states of light have implications for precision measurement in areas as wide ranging as such as gravitational wave sensing [1] and biological imaging [2]. Optical absorption estimation is the task of estimating the transmission parameter η which is defined by the ratio of input, Iin, to output, Iout, intensity of light from a sample of interest (Iout = ηΙίη). The optimal quantum strategy provides a quantum advantage (per incident photon) of 1/(1-η) over the best classical strategy [3]. This technique has been demonstrated experimentally in single parameter estimation and imaging scenarios [4,5].