Degree

Doctor of Philosophy (PhD)

Department

Physics and Astronomy

Document Type

Dissertation

Abstract

Fisher information is a statistical metric whose inverse represents a lower bound on the variance of an unbiased estimator. Naturally, in order to make the best estimates of a given unknown parameter, one would desire to find ways to minimize the value of this lower bound. Thus, the Fisher information can also be used to compare the quality of different estimators for a given parameter: whichever estimator has a lower value for its Fisher information must also provide better estimates. The same holds true in the framework of quantum information theory, where an analog to the Fisher information, dubbed quantum Fisher information, performs the same role as its classical counterpart. This dissertation concerns itself with both types of Fisher information, and so I present two projects in which Fisher information was a helpful tool for determining the quality of our work.

In the first project, we examined potential solutions to the problem of optical loss in long-baseline interferometers, which creates a bottleneck in the resolution these arrays of telescopes can achieve. What we suggested was a novel entanglement-assisted scheme that interferes a two-mode squeezed vacuum state with the target astronomical state, and then measures the resulting state by means of homodyne detection. Ultimately, we showed that when the Fisher information is observed, our proposed scheme did not outperform the traditional schemes used in long-baseline interferometry.

In the second project, we sought to write code that could determine how to best use dynamical decoupling pulses to correct dephasing error in a nitrogen-vacancy center realization of a memory and spectator qubit system. Through the use of the Python coding language, we were able to write programs that could determine the characteristic time and model the change in fidelity of the system when XY4 pulses are applied. Ultimately, we found that the quantum fidelity of our model closely mirrored the fidelity decay function our system was expected to follow in the case where XY4 pulses are applied.

Date

4-2-2025

Committee Chair

Hwang Lee

DOI

10.31390/gradschool_dissertations.6768

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