Title: Quantum information theory
Authors:M. A. Nielsen
(Submitted on 9 Nov 2000)
Abstract: Quantum information theory is the study of the achievable limits of information processing within quantum mechanics. Many different types of information can be accommodated within quantum mechanics, including classical information, coherent quantum information, and entanglement. Exploring the rich variety of capabilities allowed by these types of information is the subject of quantum information theory, and of this Dissertation. In particular, I demonstrate several novel limits to the information processing ability of quantum mechanics. Results of especial interest include: the demonstration of limitations to the class of measurements which may be performed in quantum mechanics; a capacity theorem giving achievable limits to the transmission of classical information through a two-way noiseless quantum channel; resource bounds on distributed quantum computation; a new proof of the quantum noiseless channel coding theorem; an information-theoretic characterization of the conditions under which quantum error-correction may be achieved; an analysis of the thermodynamic limits to quantum error-correction, and new bounds on channel capacity for noisy quantum channels.
Submission historyFrom: Michael Nielsen [view email]
[v1] Thu, 9 Nov 2000 17:19:13 GMT (393kb)
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Perspectives in Quantum Physics:
Epistemological, Ontological and Pedagogical
An investigation into student and expert perspectives on the physical interpretation of quantum mechanics,
with implications for modern physics instruction.
ABSTRACT: A common learning goal for modern physics instructors is for students to recognize a difference between the experimental uncertainty of classical physics and the fundamental uncertainty of quantum mechanics. Our studies suggest this notoriously difficult task may be frustrated by the intuitively realist perspectives of introductory students, and a lack of ontological flexibility in their conceptions of light and matter. We have developed a framework for understanding and characterizing student perspectives on the physical interpretation of quantum mechanics, and demonstrate the differential impact on student thinking of the myriad ways instructors approach interpretive themes in their introductory courses. Like expert physicists, students interpret quantum phenomena differently, and these interpretations are significantly influenced by their overall stances on questions central to the so-called measurement problem: Is the wave function physically real, or simply a mathematical tool? Is the collapse of the wave function an ad hoc rule, or a physical transition not described by any equation? Does an electron, being a form of matter, exist as a localized particle at all times? These questions, which are of personal and academic interest to our students, are largely only superficially addressed in our introductory courses, often for fear of opening a Pandora’s Box of student questions, none of which have easy answers. We show how a transformed modern physics curriculum (recently implemented at the University of Colorado) may positively impact student perspectives on indeterminacy and wave-particle duality, by making questions of classical and quantum reality a central theme of our course, but also by making the beliefs of our students, and not just those of scientists, an explicit topic of discussion.
A short (4 pg.) paper describing these modern physics course transformations: "Interpretive Themes in Quantum Physics: Curriculum Development and Outcomes".
The modern physics course materials associated with this dissertation project are available for the use of educators and researchers.
As a single PDF document (13 MB)
Table of Contents Chapter 1 - Perspectives in Quantum Physics I. Introduction 1 A. Notions of Classical and Quantum Reality 1 B. Philosophy or Science? 4 C. Wave-Particle Duality and Ontological Flexibility 7 II. Epistemology and Ontology in Physics Instruction 17 III. Motivation and Overview of Dissertation Project 20 References (Chapter 1) 29 Chapter 2 - Development of Student Perspectives - Initial Studies I. Introduction 37 II. Studies 37 A. Student ideas about measurement change over time 38 B. Instructional choices influence student perspectives 41 C. Consistency of student perspectives 45 III. Summary and Discussion 46 References (Chapter 2) 48 Chapter 3 - Quantum Interpretation as Hidden Curriculum
- Variations in Instructional Practices and Associated Student Outcomes
I. Introduction 51 II. Instructors approach quantum interpretation differently 53 III. Comparing Instructor Practices (A Closer Look) 56 A. Background on course materials and curriculum similarities 56 B. Differences in instructional approaches 57 C. The double-slit experiment with single quanta 62 D. (In)consistency of student responses 65 IV. Summary and Discussion 67 References (Chapter 3) 69 Chapter 4 - Refined Characterizations of Student Perspectives on Quantum Physics I. Introduction 71 II. Interview participants and course characteristics 72 III. Refined characterizations of student perspectives 74 A. Discussion of formal interpretations 75 B. Students express beliefs that parallel expert proponents 75 C. Categorization and summary of student responses 80 IV. Summary and Discussion 87 References (Chapter 4) 91 Chapter 5 - Teaching Quantum Interpretations – Curriculum Development and Implementation I. Introduction 93 II. Curriculum Development and Implementation 94 A. Assessing incoming student perspectives and conceptual understanding 99 B. Lecture Materials 106 C. Homework 120 D. Exam Materials 125 E. Assessing outgoing perspectives 129 F. Final Essay 136 References (Chapter 5) 138 Chapter 6 - Teaching Quantum Interpretations – Comparative Outcomes and Curriculum Refinement I. Introduction 141 II. Comparative Outcomes 141 A. Student Interest in Quantum Mechanics 142 B. Interpretive Attitudes 144 III. Curriculum Refinement and Other Future Directions 151 A. Single-Photon Experiments 152 B. Entanglement and Correlated Measurementss 159 C. Atomic Models and Probability 160 IV. Concluding Remarks 162 References (Chapter 6) 165 Bibliography 167 Appendix A - Evolution of Online Survey Items
(4 pages - pdf - 330 kB)
Appendix B - Interview Protocol (Spring 2009)
(3 pages - pdf - 335 kB)
Appendix C - Selected Modern Physics Course Materials (Fall 2010)
(76 pages - pdf - 5.4 MB) - password protected*
Appendix D - Selected Homework, Exam, Survey and Final Essay Submissions from Four Students (Fall 2010)
(65 pages - pdf - 2.2 MB) - password protected*
Appendix E - Collected Excerpts from Student Reflections (Fall 2010)
(22 pages - pdf - 250 kB) - password protected*
Appendix F - Selected Student Discussion Threads (Fall 2010)
(21 pages - pdf - 790 kB) - password protected*
*Contact Charles.Baily "at" Colorado.EDU for access to password-protected links.