Physics & Astronomy ETDs

Publication Date

Summer 7-29-2019

Abstract

Quantum information science can deliver its promises in technology if we have access to near-perfect quantum states, quantum channels, and readout. These are the building blocks of any quantum informatics in computation, communication, and simulation. Invasiveness of quantum measurement is one of the major challenges in this realm. The fact that after a measurement the quantum state changes is now a rule of the game. We need smart ways to gain information about a quantum state, given finite resources, in order to characterize it prior to any task.

In this dissertation, we realize the optimal way to do quantum state tomography of qubits. We prove that a sequence of collective, isotropic weak measurements of the spins implements a POVM (Positive Operator Valued Measure) proven to be optimal. This can be categorized as an implementation of SU(2) coherent state measurement of the collective spin. Implementation of coherent state measurements for compact and noncompact Lie groups is one of the aims of this dissertation.

We aim to generalize the reconstruction of one-body density matrix in an ensemble to two-body density matrix in order to characterize the correlations among the qubits in a symmetric ensemble. This problem is more tractable, surprisingly, in infinite-dimensional Hilbert space and the realm of continuous variables. Therefore, we studied the implementation of generalized coherent state measurement of the group SU(1,1) which is the nontrivial generalization of our result for SU(2). The noncompactness of this Lie group though makes it non-trivial to implement a measurement in the over-complete basis of SU(1,1). However, we study how such a strategy would be useful in phase estimation and quantum state preparation. The latter means that measurement can resemble the task of complex control requirements for preparing states such as Schr{\"o}dinger cat state, which is of great importance in quantum communication and information.

Degree Name

Physics

Level of Degree

Doctoral

Department Name

Physics & Astronomy

First Committee Member (Chair)

Ivan Deutsch

Second Committee Member

Poul Jessen

Third Committee Member

Fransisco Elohim Becerra

Fourth Committee Member

Sudhakar Prasad

Project Sponsors

National Science Foundation

Language

English

Keywords

quantum measurement, coherent state measurement, quantum state tomography, quantum state preparation, spin squeezing

Document Type

Dissertation

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