Doctor of Philosophy (PhD)
Physics and Astronomy
This is a two-part thesis strung together by a common underlying theme—quantum correlations. We present some new characterizations and quantifications of quantum correlations and an application of one such correlation—entanglement—for quantum technology.
In Part I of the thesis, we use a Rényi generalization of the quantum conditional mutual information (QCMI) to define and study new measures of quantum entanglement and quantum discord. In particular, using a quantity derived from a Rényi QCMI, we introduce: a) the geometric squashed entanglement, a faithful entanglement measure, which is a lower bound on the squashed entanglement and which reduces to the geometric measure of entanglement for pure quantum states, b) the surprisal of measurement recoverability, a discord-like measure, which is similarly a lower bound on the quantum discord. The surprisal of measurement recoverability enhances our understanding of quantum discord in terms of the ability to recover one share of a bipartite quantum system after it has been measured.
In Part II, we discuss entanglement-enhanced quantum sensing. In particular, we consider optical interferometric sensors that use photon-number parity detection. Using the quantum and classical Cramér-Rao bounds (QCRB and CCRB) on phase precision as the figures of merit, we characterize a class of two-mode pure states for which photon-number parity measurement is optimal for phase estimation. These states turn out to be a subset of the class of path-symmetric states—a class for which photon-number counting-based measurements are known to be optimal. Further, we gauge the performance of the particular interferometry based on coherent light mixed with squeezed vacuum light and photon-number parity measurement. We show that photon-number parity is an optimal measurement for the above state in the sense that the detection scheme is capable of achieving the best phase precision offered by the state (given by its QCRB). The state by itself is also known to be capable of optimal phase precision for any state in linear interferometry for a given photon budget, called the Heisenberg limit. Thus, we demonstrate Heisenberg-limited phase estimation for the state with photon-number parity detection.
Document Availability at the Time of Submission
Release the entire work immediately for access worldwide.
Seshadreesan, Kaushik Parasuram, "Rényi Quantum Conditional Mutual Information and Parity Quantum Optical Metrology" (2015). LSU Doctoral Dissertations. 2590.
Dowling, Jonathan P.