Linear Optical Quantum Metrology with Single Photons: Exploiting Spontaneously Generated Entanglement to Beat the Shot-Noise Limit

Abstract

Quantum number-path entanglement is a resource for super-sensitive quantum metrology and in particular provides for sub-shotnoise or even Heisenberg-limited sensitivity. However, such numberpath entanglement has thought to have been resource intensive to create in the first place -typically requiring either very strong nonlinearities, or nondeterministic preparation schemes with feedforward, which are difficult to implement. Very recently, arising from the study of quantum random walks with multi-photon walkers, as well as the study of the computational complexity of passive linear optical interferometers fed with single-photon inputs, it has been shown that such passive linear optical devices generate a superexponentially large amount of number-path entanglement. A logical question to ask is whether this entanglement may be exploited for quantum metrology. We answer that question here in the affirmative by showing that a simple, passive, linear-optical interferometer -fed with only uncorrelated, single-photon inputs, coupled with simple, single-mode, disjoint photodetection -is capable of significantly beating the shotnoise limit. Our result implies a pathway forward to practical quantum metrology with readily available technology.Ever since the early work of Yurke & Yuen it has been understood that quantum number-path entanglement is a resource for super-sensitive quantum metrology, allowing for sensors that beat the shotnoise limit [1,2] [7], protein concentration measurements [8], and microscopy [9,10]. This line of work culminated in the analysis of the bosonic NOON state ((|N, 0 + |0, N )/ √ 2, where N is the total number of photons), which was shown to be optimal for local phase estimation with a fixed, finite number of photons, and in fact allows one to hit the Heisenberg limit and the Quantum Cramér-Rao Bound [11][12][13][14].Let us consider the NOON state as an example, where for this state in a two-mode interferometer we have the condition of all N particles in the first mode (and none in the second mode) superimposed with all N particles in the second mode (and none in the first mode). While such a state is known to be optimal for sensing, its generation is also known to be highly problematic and resource intensive. There are two routes to preparing high-NOON states: the first is to deploy very strong optical nonlinearities [15,16], and the second is to prepare them using measurement and feed-forward [17][18][19]. In many ways * motesk@gmail.com † dr.rohde@gmail.com; URL: http://www.peterrohde.org then NOON-state generators have had much in common with all-optical quantum computers and therefore are just as difficult to build [20]. In addition to the complicated state preparation, typically a complicated measurement scheme, such as parity measurement at each output port, also had to be deployed [21].Recently two independent lines of research, the study of quantum random walks with multi-photon walkers in passive linear-optical interferometers [22][23][24], as well as the quantum complexity analysis o...

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