This dissertation concerns itself with the virtues and vices of weak measurements. Weak measurements are all around us, but this does not mean that one should manufacture weakness on all occasions. We critically evaluate two proposals that claim weak measurements provide a novel means of performing quantum state tomography, allegedly increasing tomographic efficacy and yielding foundational insights into the nature of quantum mechanics. We find weak measurements are not an essential ingredient for most of their advertised features. In contrast to this negative finding, we highlight an optimal tomographic scheme for which weak continuous measurements are the best known implementation, taking the opportunity to present this result in the language of quantum noise.
Weak measurements are also used to describe continuous measurements and the associated unconditional and conditional master equations. Though this description has been presented before, we provide a new perspective by using tools and terminology from the discipline of quantum information and quantum computing. We do so by showing how the continuous-time evolution of these master equations arises from discretizing in time the interaction between a system and a probe field and by formulating quantum-circuit diagrams for the discretized evolution. We then reformulate this interaction by replacing the probe field with a bath of qubits, one for each discretized time segment, reproducing all of the standard quantum-optical master equations. This provides an economical formulation of the white-noise theory of continuous measurements, highlighting its fundamental underlying assumptions and limitations.
White-noise theory is incapable of describing photon-counting measurements in the presence of thermal and squeezed noise. We accommodate such scenarios by considering an environment that includes traveling wave packets that are squeezed, deriving a hierarchy of equations similar to those used to describe traveling wave packets with fixed photon number. Squeezing introduces qualitatively different effects, however, complicating numerical solution of these hierarchies. We provide preliminary numerical analysis of the formalism and showcase its utility by calculating the resonance fluorescence of a two-level atom in squeezed vacuum with squeezing bandwidth narrower than the atomic linewidth, a regime previous techniques cannot explore.
Level of Degree
Physics & Astronomy
First Committee Member (Chair)
Dr. Carlton Caves
Second Committee Member
Dr. Ivan Deutsch
Third Committee Member
Dr. Akimasa Miyake
Fourth Committee Member
Dr. Terry Loring
quantum state tomography, stochastic differential equations, quantum optics, quantum measurement theory, squeezed light
Gross, Jonathan A.. "Weak measurements for quantum characterization and control." (2018). https://digitalrepository.unm.edu/phyc_etds/204