Measurement of transmission coefficient and phase shift in quantum interferometry

We present an interferometric setup designed to measure the transmission coefficient T of an object, analyzing its implications within the framework of quantum metrology. To the best of our knowledge, this is the first theoretical study to investigate the precision of transmission coefficient estimation in such a configuration. Typically, the phase difference of arms is focal point; however, our work specifically addresses the highest achievable estimation accuracy of the object’s transmission coefficient T and phase γ it introduces. Through a detailed analysis of various quantum states, including coherent, entangled coherent, Fock, and NOON states, we derive the standard deviations of these parameters by inverting the quantum Fisher information matrix. Regarding Δ γ , the entangled coherent state yields the minimum uncertainty compared to other input states, with performance improving as the number of photons increases. For Δ T , both Fock and NOON states achieve identical and optimal precision, which is also enhanced by a higher photon number. For the NOON state, the valid uncertainty range shrinks as the photon number increases, whereas for other inputs, this region expands.