Quantum-enhanced tomography of unitary processes

Abstract

This is the final published version of the article (version of record). It first appeared online via OSA at https://www.osapublishing.org/optica/abstract.cfm?uri=optica-2-6-510. Please refer to any applicable terms of use of the publisher. University of Bristol -Explore Bristol Research General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. 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.

Experimental multiphase estimation on a chip

“…Indeed, the capability of obtaining quantum-enhanced performances in the multiparameter case is particularly relevant [9], since a large variety of estimation problems involve more than a single physical quantity. Notable examples are phase imaging [10][11][12], measurements on biological systems [13,14], magnetic field imaging [15], gravitational waves parameters estimation [16,17], sensing technologies [18,19], quantum sensing networks [20], quantum process tomography [21][22][23][24] and state estimation [25].…”

“…In the last few years, several theoretical investigations on multiparameter estimation have been reported [9,31,[34][35][36][37][38][39], while experimental tests are surprisingly few. These include the simultaneous estimation of phase and its diffusion noise [40][41][42], phase and quality of the probe state [43], the discrimination of an actual signal from parasitic interference [44], and quantum-enhanced tomography of an unknown unitary process by multiphoton states [21].…”

Optimizing the Choice of Spin-Squeezed States for Detecting and Characterizing Quantum Processes

“…N00N states are maximally sensitive to small Uð1Þ phase shifts [5], but they are fragile. Other parameters might be best detected or estimated by a different optimal state [6,7], and for estimating even a simple three-parameter SUð2Þ process, the optimal state is unknown [8]. At the opposite extreme of metrology is quantum process tomography (QPT) [9,10].…”

A search algorithm for quantum state engineering and metrology

“…We are then left with the single mode final state y ñ | f . Recent progress in PNRD has made detections of larger numbers of photons possible, and transition edge sensors can now resolve at least four photons to a reasonable efficiency [8,41], whereas simpler detectors can reliably measure one or two photons [42][43][44]. The heralding number measurements we include in the toolbox are therefore á | 1 , á | 2 , á | 3 and á | 4 .…”