Negative Quantum Channels.

Cover -- Copyright Page -- Title Page -- Dedication -- Contents -- Preface -- Acknowledgments -- Introduction and Definition of Terms -- Motivation -- Open Systems -- Density Matrix -- Mathematical Structure of Open Systems -- System State Spaces -- Partial Trace -- Assignments of Subsystem States -- Reduced System Dynamics -- Vector of States'' Notation -- Tomography -- Non-Positive Reduced Dynamics -- Two Qubit SWAP Example -- Positivity Domains Interpretation -- Complete Positivity -- Complete Positivity Definition -- Reduced System Evolution as an Operator Sum -- Physical Motivation of Complete Positivity -- Total Domain Argument -- Product State Argument -- Measures of Complete Positivity -- Local Unitary Composite Evolution -- Product Composite States -- Zero Discord Initial Composite States -- Completely Positive Reduced Dynamics without a Special Form -- Choi's Matrix -- Negativity -- Negative Channels -- Definitions -- Sharp Operations for Negative Channels -- Negative Climates with Diagonal Composite Dynamics -- Specific Negative Channel Example: (,( H_d::H_d),D) -- (,( H_d::H_d),D) Basis Dependence -- Rabi Channels -- Rabi Model -- Rabi Channels with No Coupling -- Rabi Channels with Coupling -- Physical Motivations for Sharp Operations -- Negative Qubit Channel Examples with Multi-Qubit Baths -- Proposed Experimental Demonstration of Negativity -- Photonic Root-Swap Operation -- Photonic CZ Operation -- Implications of Negative Channels -- Existing Experimental Evidence of Negative Channels -- Restrictions Implied by Complete Positivity -- Expanding the Definition of ``Physically Reasonable'' -- Uses for Negative Channels -- Probing the Bath -- Coupling Alone -- Correlation Alone -- Coupling and Correlation Together -- Determining the Completely Positive Parameter Space -- Speculation on Utilities -- Conclusions.

Complete Positivity in Recent Years -- Closing Remarks -- Discussions -- Discussion of the Reduced System Definition -- General Reduced System Dynamics -- General Form of Initial Reduced System State -- Completeness Relation for _q -- Rabi Model Derivation -- Bibliography -- Author's Biography.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.