Date of Award

Spring 1-1-2018

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

First Advisor

Martin Walter

Second Advisor

Markus J. Pflaum

Third Advisor

Graeme Smith

Fourth Advisor

Judith Packer

Fifth Advisor

Arlan Ramsay

Abstract

We construct a classical code, called a Heisenberg code, which is not uniquely decipherable in order to mimic the quantum behavior of uncertainty. We classify this code according to two properties and determine the possible codeword lengths for a Heisenberg code. We suggest a possible example of a physical system which utilizes Heisenberg codes. We define a channel for Heisenberg codes, called a Heisenberg channel, which is a composite of a sender state and a receiver state which are matrices of probability amplitudes. We demonstrate that Heisenberg channels have partial trace properties similar to density matrices for quantum states. Next, we show that certain Heisenberg channels can be associated to the correlations between different partite systems of a quantum states, and define Heisenberg states and Heisenberg density matrices which are sender states and Heisenberg channels with complex entries, respectively. We prove that a Heisenberg state exists for any quantum state and that a Heisenberg density matrix relating to an n-qubit quantum state is itself a density matrix for a (2n − 1)-qubit quantum state.

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