Interferometric measurement of the quadrature coherence scale using two replicas of a quantum optical state

Assessing whether a quantum state $\widehat{\rho }$ is nonclassical ($\mathit{\text{i.e.}}$, incompatible with a mixture of coherent states) is a ubiquitous question in quantum optics, yet a nontrivial experimental task because many nonclassicality witnesses are nonlinear in $\widehat{\rho }$. In particular, if we want to witness or measure the nonclassicality of a state by evaluating its quadrature coherence scale, this $\mathit{\text{a}}\mathit{\text{priori}}$ requires full state tomography. Here, we provide an experimental procedure for directly accessing this quantity with a simple linear interferometer involving two replicas (independent and identical copies) of the state $\widehat{\rho }$ supplemented with photon-number-resolving measurements. This finding, which we interpret as an extension of the Hong-Ou-Mandel effect, illustrates the wide applicability of the multicopy interferometric technique in order to circumvent state tomography in quantum optics.