Dr Danilo Zia

Interferometric imaging of amplitude and phase of spatial biphoton states

Characterizing states of high dimensionality is a pivotal task in quantum information due to the wide range of their applications and the benefits brought in terms of security and amount of information transmitted. This task normally requires a number of projective measurements that scale exponentially with the system’s dimensionality. In this work, we address the problem of reconstructing high-dimensional quantum states in spatially correlated photon pairs emitted via a nonlinear crystal by means of a coincidence imaging approach. We implemented an innovative protocol to overcome the limitations of the full spatial mode characterization of photon pairs, that has hitherto suffered from the inefficiency and losses of detection schemes and the extreme sensitivity to the alignment of the measurement setup. In particular, we show how, for spatially correlated two-photon states, these difficulties can be surpassed by a bi-photon interferometric approach, where the unknown quantum state is superimposed with a reference one. Coincidence imaging of the resulting superposition collected with a single photon sensitive time-stamping camera allows us to retrieve the full biphoton wave function. We perform this analysis for different cases of two-photon states generated by a structured pump beam that induces spontaneous parametric down-conversion in the nonlinear crystal. From the resulting retrieved state, we show how to investigate different features of it, like the decomposition in arbitrary sets of spatial modes, orbital angular momentum correlations, certification of high-dimensional Bell states, parity conservation, and radial mode correlations. Moreover, we provide an example of the use of our approach for phase-encoded image reconstruction, which could have beneficial applications in quantum imaging protocols. The results show remarkable advantages with respect to recently developed techniques, based on projective measurements, in terms of fidelity, noise reduction, measurement time (reduced by three orders of magnitude), and accessibility to subspaces of different dimensionality. Our findings introduce a new approach to benchmark complex quantum states and open a new route toward unexplored quantum imaging and metrology techniques.