Quantum-enhanced tomography of unitary processes

A fundamental task in photonics is to characterize an unknown optical process, defined by properties such as birefringence, spectral response, thickness and flatness. Among many ways to achieve this, single-photon probes can be used in a method called quantum process tomography (QPT). However, the precision of QPT is limited by unavoidable shot noise when implemented using single-photon probes or laser light. In situations where measurement resources are limited, for example, where the process (sample) to be probed is very delicate such that the exposure to light has a detrimental effect on the sample, it becomes essential to overcome this precision limit. Here we devise a scheme for process tomography with a quantum-enhanced precision by drawing upon techniques from quantum metrology. We implement a proof-of-principle experiment to demonstrate this scheme—four-photon quantum states are used to probe an unknown arbitrary unitary process realized with an arbitrary polarization rotation. Our results show a substantial reduction of statistical fluctuations compared to traditional QPT methods—in the ideal case, one four-photon probe state yields the same amount of statistical information as twelve single probe photons.