SIAM Review
A Finite Orthomodular Lattice Which Does Not Admit a Full Set of States
Mary Katherine Bennett
Published Apr 1, 1970• 16 citations
Abstract
Previous article Next article A Finite Orthomodular Lattice Which Does Not Admit a Full Set of StatesMary Katherine BennettMary Katherine Bennetthttps://doi.org/10.1137/1012047PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Garrett Birkhoff and , John von Neumann, The logic of quantum mechanics, Ann. of Math. (2), 37 (1936), 823–843 MR1503312 0015.14603 CrossrefGoogle Scholar[2] Samuel S. Holland, Jr., J. Abbott, The current interest in orthomodular latticesTrends in Lattice Theory (Sympos., U.S. Naval Academy, Annapolis, Md., 1966), Van Nostrand Reinhold, New York, 1970, 41–126 MR0272688 Google Scholar[3] A. N. Kolmogorov, Foundations of the theory of probability, Chelsea Publishing Co., New York, 1956viii+84 MR0079843 0074.12202 Google Scholar[4] George W. Mackey, The mathematical foundations of quantum mechanics: A lecture-note volume, W., A. Benjamin, Inc., New York-Amsterdam, 1963x+137 MR0155567 0114.44002 Google Scholar[5] C. Randall, A Mathematical Foundation for Empirical Science with Special Reference to Quantum Theory. Part I: A Calculus of Experimental Propositions, Tech. Rep., KAPL-3147, Knolls Atomic Power Laboratory, 1966 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Noncontextual coloring of orthogonality hypergraphsJournal of Mathematical Physics, Vol. 63, No. 3 | 1 Mar 2022 Cross Ref Bibliography on quantum logics and related structuresInternational Journal of Theoretical Physics, Vol. 31, No. 3 | 1 Mar 1992 Cross Ref Orthomodular Lattices and Quadratic Spaces: A SurveyRocky Mountain Journal of Mathematics, Vol. 21, No. 3 | 1 Sep 1991 Cross Ref Automorphism groups and the full state spaces of the Petersen graph generalizations of G32Discrete Mathematics, Vol. 70, No. 2 | 1 Jan 1988 Cross Ref BACK MATTERMeasures and Hilbert Lattices | 29 May 2013 Cross Ref SPIN MANUALS: EMPIRICAL LOGIC TALKS QUANTUM MECHANICSMathematical Foundations of Quantum Theory | 1 Jan 1978 Cross Ref Some results from the combinatorial approach to quantum logicSynthese, Vol. 29, No. 1-4 | 1 Dec 1974 Cross Ref BIBLIOGRAPHYResiduation Theory | 1 Jan 1972 Cross Ref Orthomodular lattices admitting no statesJournal of Combinatorial Theory, Series A, Vol. 10, No. 2 | 1 Mar 1971 Cross Ref Volume 12, Issue 2| 1970SIAM Review175-324 History Submitted:31 October 1967Published online:18 July 2006 InformationCopyright © 1970 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1012047Article page range:pp. 267-271ISSN (print):0036-1445ISSN (online):1095-7200Publisher:Society for Industrial and Applied Mathematics
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Previous article Next article A Finite Orthomodular Lattice Which Does Not Admit a Full Set of StatesMary Katherine BennettMary Katherine Bennetthttps://doi.org/10.1137/1012047PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Garrett Birkhoff and , John von Neumann, The logic of quantum mechanics, Ann. of Math. (2), 37 (1936), 823–843 MR1503312 0015.14603 CrossrefGoogle Scholar[2] Samuel S. Holland, Jr., J. Abbott, The current interest in orthomodular latticesTrends in Lattice Theory (Sympos., U.S. Naval Academy, Annapolis, Md., 1966), Van Nostrand Reinhold, New York, 1970, 41–126 MR0272688 Google Scholar[3] A. N. Kolmogorov, Foundations of the theory of probability, Chelsea Publishing Co., New York, 1956viii+84 MR0079843 0074.12202 Google Scholar[4] George W. Mackey, The mathematical foundations of quantum mechanics: A lecture-note volume, W., A. Benjamin, Inc., New York-Amsterdam, 1963x+137 MR0155567 0114.44002 Google Scholar[5] C. Randall, A Mathematical Foundation for Empirical Science with Special Reference to Quantum Theory. Part I: A Calculus of Experimental Propositions, Tech. Rep., KAPL-3147, Knolls Atomic Power Laboratory, 1966 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Noncontextual coloring of orthogonality hypergraphsJournal of Mathematical Physics, Vol. 63, No. 3 | 1 Mar 2022 Cross Ref Bibliography on quantum logics and related structuresInternational Journal of Theoretical Physics, Vol. 31, No. 3 | 1 Mar 1992 Cross Ref Orthomodular Lattices and Quadratic Spaces: A SurveyRocky Mountain Journal of Mathematics, Vol. 21, No. 3 | 1 Sep 1991 Cross Ref Automorphism groups and the full state spaces of the Petersen graph generalizations of G32Discrete Mathematics, Vol. 70, No. 2 | 1 Jan 1988 Cross Ref BACK MATTERMeasures and Hilbert Lattices | 29 May 2013 Cross Ref SPIN MANUALS: EMPIRICAL LOGIC TALKS QUANTUM MECHANICSMathematical Foundations of Quantum Theory | 1 Jan 1978 Cross Ref Some results from the combinatorial approach to quantum logicSynthese, Vol. 29, No. 1-4 | 1 Dec 1974 Cross Ref BIBLIOGRAPHYResiduation Theory | 1 Jan 1972 Cross Ref Orthomodular lattices admitting no statesJournal of Combinatorial Theory, Series A, Vol. 10, No. 2 | 1 Mar 1971 Cross Ref Volume 12, Issue 2| 1970SIAM Review175-324 History Submitted:31 October 1967Published online:18 July 2006 InformationCopyright © 1970 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1012047Article page range:pp. 267-271ISSN (print):0036-1445ISSN (online):1095-7200Publisher:Society for Industrial and Applied Mathematics
Previous article Next article Scattering Theory by the Enss Method (Peter A. Perry) (B. Simon, ed.)George A. HagedornGeorge A. Hagedornhttps://doi.org/10.1137/1027082PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout"Scattering Theory by the Enss Method (Peter A. Perry) (B. Simon, ed.)." SIAM Review, 27(2), pp. 274–275[1] Volker Enss, Asymptotic completeness for quantum mechanical potential scattering. I. Short range potentials, Comm. Math. Phys., 61 (1978), 285–291 58:25583 0389.47005 CrossrefISIGoogle Scholar[2] Volker Enss, P. Blanchard, Completeness of three-body quantum scatteringDynamics and processes (Bielefeld, 1981), Lecture Notes in Math., Vol. 1031, Springer, Berlin, 1983, 62–88, Heidelberg–New York 85h:81071 0531.47009 CrossrefGoogle Scholar[3] P. Lax and , R. S. Phillips, Scattering theory, Pure and Applied Mathematics, Vol. 26, Academic Press, New York, 1967xii+276 pp. (1 plate) 36:530 0186.16301 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Volume 27, Issue 2| 1985SIAM Review History Published online:02 August 2006 InformationCopyright © 1985 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1027082Article page range:pp. 274-275ISSN (print):0036-1445ISSN (online):1095-7200Publisher:Society for Industrial and Applied Mathematics
Previous article Next article Minimax Measurements in a General Statistical Decision TheoryN. A. BogomolovN. A. Bogomolovhttps://doi.org/10.1137/1126084PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Abraham Wald, Statistical Decision Functions, John Wiley & Sons Inc., New York, N. Y., 1950ix+179 12,193f 0040.36402 Google Scholar[2] C. W. Helstrom, Quantum Detection and Estimation Theory, Academic Press, New York, 1976 Google Scholar[3] A. S. Kholevo, Investigations in the general theory of statistical decisions, Proc. Steklov Inst. Math., 124 (1976), , (In Russian.) 0497.62010 Google Scholar[4] M. Ozawa, Optimal measurements for general quantum systems, Rep. Math. Phys., 18 (1980), 11–28 10.1016/0034-4877(80)90036-1 84m:81026 0571.46051 CrossrefGoogle Scholar[5] N. N. Chentsov, Statistical Decision Rules and Optimal Inference, American Mathematical Society, Providence, RI, 1981 Google Scholar[6] N. Bourbaki, General Topology : Topological Groups, Numbers, and the Groups and Spaces Related to Them, Addison-Wesley, Reading, MA, 1966 Google Scholar[7] V. S. Varadaraian, Measures on topological spaces, Amer. Math. Soc. Transl.(2), 48 (1965), 161–228 Google Scholar[8] Michael Reed and , Barry Simon, Methods of modern mathematical physics. I. Functional analysis, Academic Press, New York, 1972xvii+325 58:12429a 0242.46001 Google Scholar[9] E. Hewitt and , K. Ross, Abstract Harmonic Analysis, Vol. 1, Springer-Verlag, Berlin-New York, 1963 0830.43001 CrossrefGoogle Scholar[10] Paul R. Halmos, Measure Theory, D. Van Nostrand Company, Inc., New York, N. Y., 1950xi+304 11,504d 0040.16802 CrossrefGoogle Scholar[11] Frederick P. Greenleaf, Invariant means on topological groups and their applications, Van Nostrand Mathematical Studies, No. 16, Van Nostrand Reinhold Co., New York, 1969ix+113 40:4776 0174.19001 Google Scholar[12] A. S. Holevo (Kholevo), Estimation of shift parameters of a quantum state, Rep. Math. Phys., 13 (1978), 379–399 10.1016/0034-4877(78)90065-4 80a:81060 0402.47006 CrossrefGoogle Scholar[13] Oscar Wesler, Invariance theory and a modified minimax principle, Ann. Math. Statist., 30 (1959), 1–20 21:5263 0089.14501 CrossrefGoogle Scholar[14] L. LeCam, An extension of Wald's theory of statistical decision functions, Ann. Math. Statist., 26 (1955), 69–81 16,730d 0064.38702 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Multiple-Phase Quantum Interferometry: Real and Apparent Gains of Measuring All the Phases Simultaneously27 January 2022 | Physical Review Letters, Vol. 128, No. 4 Cross Ref Minimax quantum state estimation under Bregman divergence4 March 2019 | Quantum, Vol. 3 Cross Ref Quantum Information Geometry and Quantum Estimation4 November 2016 Cross Ref Fourier Analytic Approach to Quantum Estimation of Group Action16 August 2016 | Communications in Mathematical Physics, Vol. 347, No. 1 Cross Ref Quantum Hypothesis Testing for Gaussian States: Quantum Analogues of χ2, t-, and F-Tests5 February 2013 | Communications in Mathematical Physics, Vol. 318, No. 2 Cross Ref Volume 26, Issue 4| 1982Theory of Probability & Its Applications History Submitted:10 November 1980Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1126084Article page range:pp. 787-795ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics
Previous article Next article Solvable Models in Quantum Mechanics (S. Albeverio, F. Gesztesy, R. Hoegh-Krohn, and H. Holden)F. H. BrownellF. H. Brownellhttps://doi.org/10.1137/1032018PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] H. Weyl, Ramifications, old and new, of the eigenvalue problem, Bull. Amer. Math. Soc., 56 (1950), 115–139 11,666i 0041.21003 CrossrefISIGoogle Scholar[2] F. H. Brownell, Spectrum of the static potential Schrödinger equation over $E\sb n$, Ann. of Math. (2), 54 (1951), 554–594 13,847a 0044.42703 CrossrefISIGoogle Scholar[3] F. A. Berezin and , L. D. Faddeev, A remark on Schrödinger's equation with a singular potential, Soviet Math. Dokl., 2 (1961), 372–375 0117.06601 Google Scholar[4] C. N. Friedman, Perturbations of the Schröedinger equation by potentials with small support, J. Functional Analysis, 10 (1972), 346–360 10.1016/0022-1236(72)90033-X 49:5529 0235.35009 CrossrefGoogle Scholar[5] F. H. Brownell, Real variables and Hilbert space operators for scientists, University Microfilms International, Ann Arbor, MI, 1978 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails On the relation between two different methods to treat Hamiltonians with point interactionsIntegral Equations and Operator Theory, Vol. 14, No. 3 Cross Ref Volume 32, Issue 1| 1990SIAM Review History Published online:18 July 2006 InformationCopyright © 1990 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1032018Article page range:pp. 160-167ISSN (print):0036-1445ISSN (online):1095-7200Publisher:Society for Industrial and Applied Mathematics