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Frontiers in Optics

Effects of Partial Coherence on Quantum-Inspired Superresolution

Kevin Liang, S. A. Wadood, A. Nick Vamivakas

Published Jan 1, 2022• 0 citations
Publisher

Abstract

Quantum Fisher information calculations show that partially coherent objects may exhibit greater precision for parameter estimation. This implies an advantage in recent quantum-inspired superresolution techniques, including spatial-mode demultiplexing.
DOI
10.1364/fio.2022.fm1c.2

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•Nov 14, 2019•44 citations
Fundamental wave features of light play an important role in the realization of superresolution for two spatially separated point sources. It has been shown that (partial) coherence, which is an inevitable feature in practical light propagation, is harmful to measurement precision thus preventing superresolution. Here we study the quantitative effect of another fundamental feature, entanglement, on the quality of superresolution and compare it with that of coherence. Both single- and two-parameter estimations are analyzed in detail. Surprisingly, contrary to coherence, it is found that superresolution measurement precision (in terms of Fisher Information) can be enhanced as the amount of entanglement increases. More importantly, our analysis shows that non-zero entanglement always guarantees the non-vanishing of Fisher Information. Thus, while coherence is unwanted, entanglement is a favorable feature for superresolution.
When two point sources are separated by less than the Abbe-Rayleigh limit, conventional resolution methods fail to distinguish whether there is one source or two. Consequently, it becomes nearly impossible to resolve important relative properties of the two sources, such as mutual coherence, relative phase, and brightness contrast. In this regime, the incoming composite quantum signal must be treated as a single entity described by an overall quantum wave function. In this study, we explore the superresolution of such two-point sources by examining a special wave property, i.e., entanglement between spatial degree of freedom (DoF) and remaining DoFs (both internal and external). Remarkably, we find that increasing this inter-DoF entanglement enhances the precision of superresolution, as quantified by the quantum Fisher information (QFI) in single-parameter estimation. Moreover, we show that this entanglement reliably ensures a nonvanishing QFI in two-parameter estimation, highlighting its role as a valuable resource for quantum superresolution.
We analyze the problem of resolving two point-sources in the case of mutually coherent sources with arbitrary quantum statistics, mutual phase, relative and absolute intensity. We use a sensitivity measure based on the method of moments and compare direct imaging with spatial mode demultiplexing, analytically proving the advantage of the latter. We show that the sensitivity of spatial mode demultiplexing saturates the quantum Fisher information, for all known cases, even for non-Gaussian states of the sources.
In recent proposals for achieving optical super-resolution, variants of the Quantum Fisher Information (QFI) quantify the attainable precision. We find that claims about a strong enhancement of the resolution resulting from coherence effects are questionable because they refer to very small subsets of the data without proper normalization. When the QFI is normalized, accounting for the strength of the signal, there is no advantage of coherent sources over incoherent ones. Our findings have a bearing on further studies of the achievable precision of optical instruments.
In recent proposals for achieving optical super-resolution, variants of the Quantum Fisher Information (QFI) quantify the attainable precision. We find that claims about a strong enhancement of the resolution resulting from coherence effects are questionable because they refer to very small subsets of the data without proper normalization. When the QFI is normalized, accounting for the strength of the signal, there is no advantage of coherent sources over incoherent ones. Our findings have a bearing on further studies of the achievable precision of optical instruments.