Quantum-enhanced tomography of unitary processes

Abstract

A fundamental task in photonics is to characterise an unknown optical\nprocess, defined by properties such as birefringence, spectral response,\nthickness and flatness. Amongst many ways to achieve this, single-photon probes\ncan be used in a method called quantum process tomography (QPT). Furthermore,\nQPT is an essential method in determining how a process acts on quantum\nmechanical states. For example for quantum technology, QPT is used to\ncharacterise multi-qubit processors and quantum communication channels; across\nquantum physics QPT of some form is often the first experimental investigation\nof a new physical process, as shown in the recent research into coherent\ntransport in biological mechanisms. However, the precision of QPT is limited by\nthe fact that measurements with single-particle probes are subject to\nunavoidable shot noise---this holds for both single photon and laser probes. In\nsituations where measurement resources are limited, for example, where the\nprocess is rapidly changing or the time bandwidth is constrained, it becomes\nessential to overcome this precision limit. Here we devise and demonstrate a\nscheme for tomography which exploits non-classical input states and quantum\ninterferences; unlike previous QPT methods our scheme capitalises upon the\npossibility to use simultaneously multiple photons per mode. The\nefficiency---quantified by precision per photon used---scales with larger\nphoton number input states. Our demonstration uses four-photon states and our\nresults show a substantial reduction of statistical fluctuations compared to\ntraditional QPT methods---in the ideal case one four-photon probe state yields\nthe same amount of statistical information as twelve single probe photons.\n