TY - BOOK

T1 - Action Formalism for Measurement Induced Dynamics: Topological and Thermal Aspects

AU - Shea, Dominic

PY - 2024

Y1 - 2024

N2 - Feynman’s path integral is a formulation of quantum mechanics akin to analogous formulations developed for stochastic processes and statistical physics. One process that combines quantum dynamics with stochastic features and constitutes a prevailing area of research is quantum measurement. Beyond past attempts, recent advancements, exemplified by the Chantasari-Dressel-Jordan (CDJ) method, explore measurement-induced dynamics in continuously monitored quantum systems.This thesis utilises the CDJ path integral to explore new emerging featuresassociated with measurement-induced dynamics. Firstly, we develop the CDJ pathintegral to analyse geometric phases. Focusing on self-closing trajectories fromcontinuous measurements, we incorporate geometric phase information directly in the path integral for a single qubit and demonstrate that the geometric phase of the most likely trajectories exhibits a topological transition as a function of measurement strength. We further address the effect of Gaussian fluctuations.Secondly, we exploit the formalism to study measurement-induced entanglementdynamics, where we combine the stochastic effect of measurements and that oflocal unitary noise. We identify the optimal entanglement dynamics and developdiagrammatic methods that produce a closed-form approximation of the average entanglement dynamics. The optimal trajectories and diagrammatic expansion capture the oscillations of entanglement at short times. We find by numerical investigation that long-time steady-state entanglement reveals a non-monotonic relationship between concurrence and noise strength.Finally, we lay the basis for applying path integrals to fluctuation theorems bydevising a suitable single qubit protocol to verify a recently proposed fluctuationtheorem that governs the statistical behaviour of quantum systems far from equilibrium. The proposed protocol is suitable for existing quantum architectures.Our results provide a basis for extending the use of fluctuation theorems to many body systems, where geometric phases and entanglement play crucial roles in classifying quantum order.

AB - Feynman’s path integral is a formulation of quantum mechanics akin to analogous formulations developed for stochastic processes and statistical physics. One process that combines quantum dynamics with stochastic features and constitutes a prevailing area of research is quantum measurement. Beyond past attempts, recent advancements, exemplified by the Chantasari-Dressel-Jordan (CDJ) method, explore measurement-induced dynamics in continuously monitored quantum systems.This thesis utilises the CDJ path integral to explore new emerging featuresassociated with measurement-induced dynamics. Firstly, we develop the CDJ pathintegral to analyse geometric phases. Focusing on self-closing trajectories fromcontinuous measurements, we incorporate geometric phase information directly in the path integral for a single qubit and demonstrate that the geometric phase of the most likely trajectories exhibits a topological transition as a function of measurement strength. We further address the effect of Gaussian fluctuations.Secondly, we exploit the formalism to study measurement-induced entanglementdynamics, where we combine the stochastic effect of measurements and that oflocal unitary noise. We identify the optimal entanglement dynamics and developdiagrammatic methods that produce a closed-form approximation of the average entanglement dynamics. The optimal trajectories and diagrammatic expansion capture the oscillations of entanglement at short times. We find by numerical investigation that long-time steady-state entanglement reveals a non-monotonic relationship between concurrence and noise strength.Finally, we lay the basis for applying path integrals to fluctuation theorems bydevising a suitable single qubit protocol to verify a recently proposed fluctuationtheorem that governs the statistical behaviour of quantum systems far from equilibrium. The proposed protocol is suitable for existing quantum architectures.Our results provide a basis for extending the use of fluctuation theorems to many body systems, where geometric phases and entanglement play crucial roles in classifying quantum order.

U2 - 10.17635/lancaster/thesis/2566

DO - 10.17635/lancaster/thesis/2566

M3 - Doctoral Thesis

PB - Lancaster University

ER -