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
Introduction and Definition of Terms
Non-Positive Reduced Dynamics
Physical Motivation of Complete Positivity
Measures of Complete Positivity
Negative Climates with Diagonal Composite Dynamics
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
About the Author(s)James M. McCracken
, George Mason University
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.