Negative Quantum Channels

This book is a brief introduction to negative quantum channels, i.e., linear, trace-preserving (and consistent) quantum maps that are not completely positive. The flat and sharp operators are introduced and explained. Complete positivity is presented as a mathematical property, but it is argued that complete positivity is not a physical requirement of all quantum operations. Negativity, a measure of the lack of complete positivity, is proposed as a tool for empirically testing complete positivity assumptions. Table of Contents: Preface / Acknowledgments / Introduction and Definition of Terms / Tomography / Non-Positive Reduced Dynamics / Complete Positivity / Physical Motivation of Complete Positivity / Measures of Complete Positivity / Negative Channels / Negative Climates with Diagonal Composite Dynamics / Rabi Channels / Physical Motivations for Sharp Operations / Negative Qubit Channel Examples with Multi-Qubit Baths / Proposed Experimental Demonstration of Negativity / Implications of Negative Channels / Uses for Negative Channels / Conclusions / Bibliography / Author's Biography

Preface.- Acknowledgments.- Introduction and Definition of Terms.- Tomography.- Non-Positive Reduced Dynamics.- Complete Positivity.- Physical Motivation of Complete Positivity.- Measures of Complete Positivity.- Negative Channels.- Negative Climates with Diagonal Composite Dynamics.- Rabi Channels.- Physical Motivations for Sharp Operations.- Negative Qubit Channel Examples with Multi-Qubit Baths.- Proposed Experimental Demonstration of Negativity.- Implications of Negative Channels.- Uses for Negative Channels.- Conclusions.- Bibliography.- Author's Biography .

James M. McCracken received his Physics M.S. studying decoherence in quantum dot qubit structures at the University of Central Florida, and he received two B.S. degrees, one in Physics and one in Astrophysics, from the Florida Institute of Technology. He was a member of both the theoretical quantum computing team at Science Applications International Corporation (SAIC) and the informatics group at the U. S. Naval Research Laboratory in Washington, DC. James is currently a Ph.D. candidate studying time series causality and geomagnetic storm prediction at George Mason University in Fairfax, Virginia.