Quantum theory: Concepts and methods

Have you ever felt that the very title, Progress in Optics, conjured an image in your mind? Don’t you see a row of handsomely printed books, bearing the editorial stamp of one of the most brilliant members of the optics community, and chronicling the field of optics since the invention of the laser? If so, you are certain to move the bookend to make room for Volume 16, the latest of this series. It contains seven chapters on widely diverging topics, written by well-known authorities in their fields. These are: 1) Laser Selective Photophysics and Photochemistry by V. S. Letokhov, 2) Recent Advances in Phase Profiles (sic) Generation by J. J. Clair and C. I. Abitbol, 3 ) Computer-Generated Holograms: Techniques and Applications by W.-H. Lee, 4) Speckle Interferometry by A. E. Ennos, 5 ) Deformation  Invariant, Space-Variant Optical  Pattern Recognition by D. Casasent and D. Psaltis, 6) Light Emission from High-Current Surface-Spark Discharges by R. E. Beverly, and 7) Semiclassical Radiation  Theory within a  QuantumMechanical Framework by I. R. Senitzkt. The  breadth of topic  matter  spanned  by  these  chapters makes it impossible, for this reviewer at least, to pass judgement on the comprehensiveness, relevance, and completeness of every chapter. With an editorial board as prominent as that of Progress in Optics, however, it seems hardly likely that such comments should be necessary. It should certainly be possible to take the authority of each author as credible. The only remaining judgment to be  made on these chapters is their readability. In short, what are they like to read? The first sentence of the first chapter greets the eye with an obvious typographical error: “The creation of coherent laser light source, that have tunable radiation, opened the . . . .” Two pages later we find: “When two types of atoms or molecules of different isotopic composition ( A and B ) have even one spectral line that does not overlap with others, it is pos-

Progress in optics

Preface Prologue 1. Introduction 2. On sets and kinds in IR 3. Vector and Hilbert spaces 4. Linear transformations, operators and matrices 5. Conditional logic in IR 6. The geometry of IR Appendix I. Linear algebra Appendix II. Quantum mechanics Appendix III. Probability Bibliography Index.

The Geometry of Information Retrieval

We use the mathematical language of sheaf theory to give a unified treatment of non-locality and contextuality, in a setting that generalizes the familiar probability tables used in non-locality theory to arbitrary measurement covers; this includes Kochen–Specker configurations and more. We show that contextuality, and non-locality as a special case, correspond exactly to obstructions to the existence of global sections. We describe a linear algebraic approach to computing these obstructions, which allows a systematic treatment of arguments for non-locality and contextuality. We distinguish a proper hierarchy of strengths of no-go theorems, and show that three leading examples—due to Bell, Hardy and Greenberger, Horne and Zeilinger, respectively—occupy successively higher levels of this hierarchy. A general correspondence is shown between the existence of local hidden-variable realizations using negative probabilities, and no-signalling; this is based on a result showing that the linear subspaces generated by the non-contextual and no-signalling models, over an arbitrary measurement cover, coincide. Maximal non-locality is generalized to maximal contextuality, and characterized in purely qualitative terms, as the non-existence of global sections in the support. A general setting is developed for the Kochen–Specker-type results, as generic, model-independent proofs of maximal contextuality, and a new combinatorial condition is given, which generalizes the ‘parity proofs’ commonly found in the literature. We also show how our abstract setting can be represented in quantum mechanics. This leads to a strengthening of the usual no-signalling theorem, which shows that quantum mechanics obeys no-signalling for arbitrary families of commuting observables, not just those represented on different factors of a tensor product.

http://iopscience.iop.org/article/10.1088/1367-2630/13/11/113036/pdf

The sheaf-theoretic structure of non-locality and contextuality

Manuscript received April 14, 1983; revised June 24, 1983. N. B. Abraham is with the Department of Physics, BrynMawr College, Bryn Mawr, PA 19010. P. Mandel is with the Service de Chimie Physique 11, Universite Libre de Bruselles, Brussels, Belgium. L. W. Casperson is with the Department of Electrical Engineering and Applied Science: University of California, Los Angeles, CA 90024. Editor’s Note: A similar correction by Dr. F. Holigner and Prof. Dr. H. Weber of the Universitat Kaiserslautern was received on May 4, 1983. tions can be expressed as BR = y + p P (3a j

Principles of lasers

Some reference citations in the text of this paper are incorrect and should be amended as listed below. The reference list is correct as published. Page 1579, line 5: [23, 34, 38, 39] should read [23, 34, 35, 36] Page 1579, line 9: [40] should read [37] Page 1580, line 8: [31, 33, 35] should read [31, 33, 38] Page 1580, line 14: [36] should read [39] Page 1580, line 36: [36] should read [39] Page 1580, line 38: [37] should read [40] Page 1580, line 42: [38] should read [35] Page 1581, line 3 of caption: [33, 35] should read [33, 38] Page 1583, line 12: [41] should read [42] Page 1587, line 9: [39] should read [36] Page 1587, line 11: [39] should read [36] Page 1587, line 18: [38, 39] should read [35, 36] Page 1587, line 37: [39] should read [36] Page 1589, line 18: [39, 46, 47] should read [36, 46, 47] Page 1590, line 2: [39] should read [36] age 1590, line 3: [39] should read [36]

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Kochen-Specker Vectors

The bibliography contains 1851 references on axiomatic structures underlying quantum mechanics, with stress on varieties of algebraico-logical, probabilistic, and operational structures for which the term quantum logics is adopted. An index of about 250 keywords picked out from the titles is included and statistics about papers, journals, and authors are presented. Monographs and proceedings on the subject are noted.

/pdf/bibliography-on-quantum-logics-and-related-structures-3emfwtvhc9.pdf

Bibliography on quantum logics and related structures

We give a new algorithm for generating Greechie diagrams with arbitrary chosennumber of atoms or blocks (with 2, 3, 4, . . . atoms) and provide a computerprogram for generating the diagrams. The results show that the previous algorithmdoes not produce every diagram and that it is atleast 105 times slower. We alsoprovide an algorithm and programs for checking Greechie diagram passage byequations defining varieties of orthomodular lattices and give examples fromHilbert lattices. We also discuss some additional characteristics of Greechiediagrams.

/pdf/algorithms-for-greechie-diagrams-5csphpzmu5.pdf

Algorithms for Greechie Diagrams

https://bib.irb.hr/datoteka/436854.arxiv-0910.1311.pdf

New Kochen–Specker sets in four dimensions

It is shown that the property of orthomodularity can be interpreted as a particular reduction of the operations of implication to the relation of implication, and a physical interpretation of the result is given.

Mladen Pavicic

Papers

Kochen-Specker Vectors

Bibliography on quantum logics and related structures

Algorithms for Greechie Diagrams

New Kochen–Specker sets in four dimensions

Minimal Quantum Logic with Merged Implications