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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 history

From: Michael Nielsen [view email]
[v1] Thu, 9 Nov 2000 17:19:13 GMT (393kb)

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Charles Baily
Ph.D. Dissertation
Spring 2011

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)


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)


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)


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)


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)


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)


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.

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