How to perform the most accurate possible phase measurements

By Dominic W. Berry, B. Higgins, Stephen D. Bartlett, Morgan W. Mitchell, G. Pryde, Howard M. Wiseman. 2009

137 citations recorded by the source corpus.

We present the theory of how to achieve phase measurements with the minimum possible variance in ways that are readily implementable with current experimental techniques. Measurements whose statistics have high-frequency fringes, such as those obtained from NOON states, have commensurately high information yield (as quantified by the Fisher information). However this information is also highly ambiguous because it does not distinguish between phases at the same point on different fringes. We provide schemes to eliminate this phase ambiguity in a highly efficient way, providing phase estimates with uncertainty that is within a small constant factor of the Heisenberg limit, the minimum allowed by the laws of quantum mechanics. These techniques apply to NOON state and multi-pass interferometry, as well as phase measurements in quantum computing. We have reported the experimental implementation of some of these schemes with multi-pass interferometry elsewhere. Here we present the theoretical foundation, and also present some new experimental results. There are three key innovations to the theory in this paper. First, we examine the intrinsic phase properties of the sequence of states (in multiple time modes) via the equivalent two-mode state. Second, we identify the key feature of the equivalent state that enables the optimal scaling of the intrinsic phase uncertainty to be obtained. This enables us to identify appropriate combinations of states to use. The remaining difficulty is that the ideal phase measurements to achieve this intrinic phase uncertainty are often not physically realizable. The third innovation is to solve this problem by using realizable measurements that closely approximate the optimal measurements, enabling the optimal scaling to be preserved. We consider both adaptive and nonadaptive measurement schemes.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/bc5b50f1f78d88eb3339d91cbdf527609978eebe

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Quantum metrology with nonclassical states of atomic ensembles (2016, background): “Note that the fast oscillations of the output probabilities obtained with the state (127) seem to prevent the unambiguous estimate of a phase larger than 2π=N (Boto et al., 2000; Mitchell, 2005; Pezzè and Smerzi, 2007; Berry et al., 2009).”
Elucidating reaction mechanisms on quantum computers (2016, methodology): “This scaling is asymptotically optimal [27] (because the Holevo variance coincides with the circular variance for narrow distributions), and as such we do not expect that an unbiased estimator of the eigenphase will be able to substantially outperform this without either the use of prior information”
Quantum limits in optical interferometry (2014, background): “…as a resource, it has been demonstrated experimentally (Higgins et al., 2007) that in the absence of noise such a device can indeed achieve the Heisenberg scaling without resorting to entanglement and efficiency of various multi-pass protocols has been analyzed in detail in (Berry et al., 2009).”
Quantum machine learning (2016, unknown): “This approach, originally proposed by Kitaev, was further reﬁned by Hig-gins, Berry et al [42, 43] who explored the use of adaptive methods to optimally learn the unknown eigenphase.”