Theoretical Limits of Quantum Ranging

Abstract

The ability to determine distances from dedicated measurements, namely active ranging, is crucial in a variety of systems including localization, radar, and lidar. This thesis establishes the quantum limits and determines the quantum advantage provided by single-beam displaced squeezed states in active ranging. Analytical expressions of the quantum Fisher information (QFI) are provided for monochromatic and continuous-mode waves passing through a thermal loss channel with arbitrary loss and noise conditions. The optimal allocation of system resources for performing displacement and squeezing operations is determined. The optimal allocation consists of apportioning all resources to perform either the displacement operation, providing no quantum advantage, or the squeezing operation. Analytical results are examined in optical and microwave regimes. The optimal gain, i.e., the ratio between the QFI obtained by optimal resource allocation and the QFI obtained by performing only the displacement operation, is derived for the optical and microwave regimes. Quantum advantage afforded by the prototypical heterodyne receiver is also investigated. The results of this thesis pave the way for establishing a foundation of active ranging and provide insights for system design employing currently available quantum technologies.