Foundational, Historical, Anecdotal and Forward-Looking Thoughts on the Quantum

This document is the first installment of three in the Cerro Grande Fire Series. It is a collection of letters written to various colleagues, most of whom regularly circuit this archive, including Howard Barnum, Paul Benioff, Charles Bennett, Herbert Bernstein, Doug Bilodeau, Gilles Brassard, Jeffrey Bub, Carlton Caves, Gregory Comer, Robert Griffiths, Adrian Kent, Rolf Landauer, Hideo Mabuchi, David Mermin, David Meyer, Michael Nielsen, Asher Peres, John Preskill, Mary Beth Ruskai, Ruediger Schack, Abner Shimony, William Wootters, Anton Zeilinger, and many others. The singular thread sewing all the letters together is the quantum. Some of the pieces are my best efforts to date to give substance to an evanescent thought I see rising from the field of quantum information---I call it the Paulian idea. To the extent I have communicated its misty shadow to my correspondents and seen a twinkle of enthusiasm, it seemed worthwhile to expand the jury on this anniversary occasion.

[1]  M. Galavotti.  Anti-realism in the philosophy of probability: Bruno de Finetti's subjectivism , 1989 .

[2]  J. Wheeler.  Genesis and Observership , 1977 .

[3]  Buzek,et al.  Quantum copying: Beyond the no-cloning theorem. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[4]  The Everett Interpretation of Quantum Mechanics. , 1971 .

[5]  Leland Gerson Neuberg,et al.  Bayes or Bust?-A Critical Examination of Bayesian Confirmation Theory. , 1994 .

[6]  William K. Wootters,et al.  Quantum mechanics without probability amplitudes , 1986 .

[7]  G. Lindblad.  On the generators of quantum dynamical semigroups , 1976 .

[8]  George Boole,et al.  An Investigation of the Laws of Thought: Frontmatter , 2009 .

[9]  John Archibald Wheeler.  World as system self-synthesized by quantum networking , 1988 .

[10]  J. Wheeler.  The computer and the universe , 1982 .

[11]  M. Strauss.  Two Concepts of Probability in Physics , 1973 .

[12]  A. Uhlmann.  The "transition probability" in the state space of a ∗-algebra , 1976 .

[13]  J. Wheeler.  ‘‘On recognizing ‘law without law,’ ’’ Oersted Medal Response at the joint APS–AAPT Meeting, New York, 25 January 1983 , 1983 .

[14]  B. Skyrms.  Probability and causation , 1988 .

[15]  Warner A. Miller,et al.  Delayed-Choice Experiments and Bohr's Elementary Quantum Phenomenon , 1997 .

[16]  Carlton M. Caves,et al.  Quantum information: How much information in a state vector? , 1996 .

[17]  Elementary Quantum Phenomenon as Building Unit , 1983 .

[18]  C. Fuchs.  Nonorthogonal Quantum States Maximize Classical Information Capacity , 1997, quant-ph/9703043.

[19]  John Archibald Wheeler,et al.  Is Physics Legislated by Cosmogony , 1974 .

[20]  R. Jozsa,et al.  Quantum Computation and Shor's Factoring Algorithm , 1996 .

[21]  T. Loredo.  From Laplace to Supernova SN 1987A: Bayesian Inference in Astrophysics , 1990 .

[22]  Satosi Watanabe.  A Model of Mind-Body Relation in Terms of Modular Logic , 1961 .

[23]  H. Folse.  The Bohr-Einstein Debate and the Philosophers’ Debate over Realism versus Anti-Realism , 1996 .

[24]  Arthur Fine.  Do correlations need to be explained , 1989 .

[25]  R. Jeffrey.  Reading probabilismo , 1989 .

[26]  R. Giere,et al.  Objective Single-Case Probabilities and the Foundations of Statistics , 1973 .

[27]  Jeffrey Bub.  Popper's propensity interpretation of probability and quantum mechanics , 1975 .

[28]  W. Wootters,et al.  Optimal detection of quantum information. , 1991, Physical review letters.

[29]  J. Wheeler.  Transcending the Law ofConservation of Leptons , 1971 .

[30]  Charles H. Bennett,et al.  Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. , 1992, Physical review letters.

[31]  Bryce S. DeWitt,et al.  The Many-Universes Interpretation of Quantum Mechanics , 2015 .

[32]  John Archibald Wheeler,et al.  Recent Thinking about the Nature of the Physical World: It from Bit a , 1992 .

[33]  John Archibald Wheeler,et al.  PREGEOMETRY: MOTIVATIONS AND PROSPECTS , 1980 .

[34]  Edward Farhi,et al.  How probability arises in quantum mechanics , 1989 .

[35]  Stanislav Sýkora,et al.  Quantum theory and the bayesian inference problems , 1974 .

[36]  John Archibald Wheeler,et al.  Include the Observer in the Wave Function , 1977 .

[37]  C. S. Sharma,et al.  A direct proof of Wigner's theorem on maps which preserve transition probabilities between pure states of quantum systems , 1990 .

[38]  Wineland,et al.  Optimal frequency measurements with maximally correlated states. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[39]  J. Cirac,et al.  Improvement of frequency standards with quantum entanglement , 1997, quant-ph/9707014.

[40]  John Archibald Wheeler,et al.  At Home in the Universe , 1994 .

[41]  Abner Shimony,et al.  The Philosophy of Niels Bohr: The Framework of Complementarity , 1985 .

[42]  A. Garrett.  Making Sense of Quantum Mechanics: Why You Should Believe in Hidden Variables , 1993 .

[43]  E. Squires.  On an alleged “proof” of the quantum probability law , 1990 .

[44]  D. Lewis.  A Subjectivist’s Guide to Objective Chance , 1980 .

[45]  W. Ochs.  On the strong law of large numbers in quantum probability theory , 1977, J. Philos. Log..

[46]  David W. Miller,et al.  Single-case probabilities , 1991 .

[47]  Unknown probabilities , 1996 .

[48]  Quantum Gravity: the Question of Measurement , 1984 .

[49]  Hood,et al.  Measurement of conditional phase shifts for quantum logic. , 1995, Physical review letters.

[50]  Concepts of convergence for a quantum law of large numbers , 1980 .

[51]  James B. Hartle,et al.  Quantum Mechanics of Individual Systems , 1968, 1907.02953.

[52]  A. Holevo.  Statistical decision theory for quantum systems , 1973 .

[53]  H. Folse.  The Copenhagen Interpretation of Quantum Theory and Whitehead’s Philosophy of Organism , 1974 .

[54]  The quantum and the universe. , 1979 .

[55]  I. Pitowsky,et al.  George Boole's ‘Conditions of Possible Experience’ and the Quantum Puzzle , 1994, The British Journal for the Philosophy of Science.

[56]  James H. Fetzer.  Statistical Probabilities: Single Case Propensities vs. Long-Run Frequencies , 1974 .

[57]  K. V. Laurikainen,et al.  Beyond the Atom: The Philosophical Thought of Wolfgang Pauli , 1988 .

[58]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[59]  Using classical probability to guarantee properties of infinite quantum sequences. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[60]  J. Wheeler.  Information, physics, quantum: the search for links , 1999 .

[61]  Roger M. Cooke,et al.  An elementary proof of Gleason's theorem , 1985, Mathematical Proceedings of the Cambridge Philosophical Society.

[62]  Schack,et al.  Information-theoretic characterization of quantum chaos. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[63]  B. Skyrms.  Statistical Laws and Personal Propensities , 1978, PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association.

[64]  A. Gleason.  Measures on the Closed Subspaces of a Hilbert Space , 1957 .

[65]  Ronald N. Giere,et al.  A laplacean formal semantics for single-case propensities , 1976, J. Philos. Log..

[66]  C. Rovelli,et al.  Relational Quantum Mechanics , 2006 .

[67]  J. Wheeler.  The Universe as Home for Man , 1974 .

[68]  I. Pitowsky.  Infinite and finite Gleason’s theorems and the logic of indeterminacy , 1998 .

[69]  Isaac Levi.  Probability Exists (But Just Barely) , 1986 .

[70]  Kurt Jacobs,et al.  Information-tradeoff relations for finite-strength quantum measurements , 2001 .

[71]  J. Wheeler.  From Relativity to Mutability , 1973 .

[72]  N. Mermin.  Hidden variables and the two theorems of John Bell , 1993, 1802.10119.

[73]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[74]  U. Uhlhorn.  REPRESENTATION OF SYMMETRY TRANSFORMATIONS IN QUANTUM MECHANICS , 1963 .

[75]  Daniel Gottesman,et al.  Stabilizer Codes and Quantum Error Correction , 1997, quant-ph/9705052.

[76]  Asher Peres,et al.  What is a state vector , 1984 .

[77]  IS QUANTUM MECHANICS A PROBABILISTIC THEORY , 1997 .

[78]  E. Jaynes.  Information Theory and Statistical Mechanics , 1957 .

[79]  E. Rose.  Beyond the Black Hole , 1989 .

[80]  Paul Humphreys,et al.  Why Propensities Cannot Be Probabilities , 1985, Philosophical Papers.

[81]  J. Wheeler.  Particles and Geometry , 1970 .

[82]  John Archibald Wheeler,et al.  The “Past” and the “Delayed-Choice” Double-Slit Experiment , 1978 .

[83]  Geoffrey Hellman.  Randomness and Reality , 1978, PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association.

[84]  M. Galavotti.  Comments on Patrick Suppes “Propensity interpretations of probability” , 1987 .

[85]  H. Folse.  Complementarity and our Knowledge of Nature , 1992 .

[86]  The Dilemmas of An Upright Man: Max Planck as Spokesman for German Science , 1986 .

[87]  “Physics as Meaning Circuit”: Three Problems , 1986 .

[88]  Hans Reichenbach,et al.  The Theory of Probability: An Inquiry into the Logical and Mathematical Foundations of the Calculus of Probability , 1971 .

[89]  N. David Mermin,et al.  What is quantum mechanics trying to tell us , 1998, quant-ph/9801057.

[90]  B. Skyrms.  Causal necessity: A pragmatic investigation of the necessity of laws , 1980 .

[91]  Itamar Pitowsky,et al.  From George Boole To John Bell — The Origins of Bell’s Inequality , 1989 .

[92]  J. Colquhoun,et al.  A matter of chance. , 1992, Australian family physician.

[93]  Asher Peres,et al.  IS QUANTUM THEORY UNIVERSALLY VALID , 1982 .

[94]  P. Suppes.  Some further remarks on propensity: Reply to Maria-Carla Galavotti , 1987 .

[95]  J. Wheeler.  Bohr’s “Phenomenon” and “Law Without Law” , 1985 .

[96]  Jan von Plato,et al.  De Finetti's earliest works on the foundations of probability , 1989 .

[97]  R. Hughes,et al.  The Structure and Interpretation of Quantum Mechanics , 1989 .

[98]  Adrian Kent,et al.  AGAINST MANY WORLDS INTERPRETATIONS , 1990 .

[99]  N. Gisin,et al.  Optimal Eavesdropping in Quantum Cryptography. I , 1997, quant-ph/9701039.

[100]  N. Gisin.  Propensities and the state‐property structure of classical and quantum systems , 1984 .

[101]  David Deutsch,et al.  Quantum theory as a universal physical theory , 1985 .

[102]  H. Dishkant,et al.  Logic of Quantum Mechanics , 1976 .

[103]  E. T. Jaynesz,et al.  Clearing up Mysteries { the Original Goal , 1989 .

[104]  H. Folse.  Laudan's Model of Axiological Change and the Bohr-Einstein Debate , 1990, PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association.

[105]  J. Wheeler,et al.  Physicist’s version of traveling salesman problem: statistical analysis , 1983 .

[106]  E. Lieb.  Convex trace functions and the Wigner-Yanase-Dyson conjecture , 1973 .

[107]  Charles H. Bennett,et al.  Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. , 1993, Physical review letters.

[108]  A brief remark on the problem of interpreting probability objectively , 1987 .

[109]  Richard Phillips Feynman,et al.  The Concept of Probability in Quantum Mechanics , 1951 .

[110]  S. Braunstein,et al.  Wringing out better bell inequalities , 1990 .

[111]  N. Mermin,et al.  The Ithaca interpretation of quantum mechanics , 1996, quant-ph/9609013.

[112]  W. Wootters,et al.  A single quantum cannot be cloned , 1982, Nature.

[113]  John Archibald Wheeler,et al.  How Come the Quantum? a , 1986 .

[114]  W. Wootters.  Entanglement of Formation of an Arbitrary State of Two Qubits , 1997, quant-ph/9709029.

[115]  J. Wheeler.  Hermann Weyl and the Unity of Knowledge , 1986 .

[116]  Charles H. Bennett,et al.  The thermodynamics of computation—a review , 1982 .

[117]  Michael D. Westmoreland,et al.  Sending classical information via noisy quantum channels , 1997 .

[118]  H. Folse.  Complementarity and the Description of Experience , 1977 .

[119]  Leslie E Ballentine,et al.  The Formulation of Quantum Mechanics , 1998 .