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Title:
Abstract:
As visual creatures, imaging systems such as telescopes and microscopes have long driven humanity's empirical scientific enterprise, allowing us to transcend our native sensory limitations. Historically, optical devices served to augment the human visual system, qualitatively enhancing our observation of small or distant features of the physical universe. Today, imaging systems have evolved to become specialized precision instruments designed to perform specific quantitative sensing tasks. In the context of this modern paradigm, we re-examine the fundamental limits of task-specific imaging through the lens of quantum information theory with particular emphasis on sub-diffraction sensing applications.
The primary obstacle limiting the precision of any instrument is noise: randomness in the outcomes of repeated experiments that cannot be accounted for, whether for practical or fundamental reasons. Quantum optics supplies a fundamental source of irreducible randomness that manifests upon measuring a state of light. The underlying probability distribution governing the random outcome of a measurement is determined by the Born Rule, which allows us to associate a statistical model to any imaging experiment. Crucially, this affords the freedom to optimize the measurement with respect to task-specific performance metrics, identifying statistical models that faithfully preserve information about parameters of interest carried by the electromagnetic field.
In this dissertation I invoke analytical tools from quantum information theory to explore the fundamental limits of three imaging challenges: (1) exoplanet discovery, (2) sub-diffraction atomic sensing (3) and generalized incoherent super-resolution imaging. In all three challenges, we find that conventional direct imaging measurements systematically fall short of these quantum limits. Instead, for relatively simple imaging problems, a nascent measurement technique known as spatial mode demultiplexing (SPADE) is shown to outperform direct imaging, often achieving quantum information-theoretic limits. For yet more complicated sensing problems involving many parameters, we find that joint detection measurements acting collectively on multiple copies of a quantum state are necessary to saturate certain quantum limits. This latter realization points to new possibilities for passive imaging systems that exploit bona fide quantum resources.
Committee:
Dr. Amit Ashok (Chair)
Dr. Dal Wilson
Dr. Daniel Soh
Dr. Saikat Guha