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Stanley Gudder [17]Stanley P. Gudder [15]
  1.  23
    Sensitivity of Entanglement Measures in Bipartite Pure Quantum States.Danko D. Georgiev & Stanley P. Gudder - 2022 - Modern Physics Letters B 36 (22):2250101.
    Entanglement measures quantify the amount of quantum entanglement that is contained in quantum states. Typically, different entanglement measures do not have to be partially ordered. The presence of a definite partial order between two entanglement measures for all quantum states, however, allows for meaningful conceptualization of sensitivity to entanglement, which will be greater for the entanglement measure that produces the larger numerical values. Here, we have investigated the partial order between the normalized versions of four entanglement measures based on Schmidt (...)
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  2. And Formal Semantics. He has Published Books as Well as Articles in Both Fields. His Work on Logic Led Him to Investigate Logical Struc-Tures Arising in Mathematical Physics. Edward Gerjuoy Professor Edward Gerjuoy BS (Physics, City College of the City. [REVIEW]Richard J. Greechie, Dick Greechie & Stanley P. Gudder - 1973 - In C. A. Hooker (ed.), Contemporary Research in the Foundations and Philosophy of Quantum Theory. Boston: D. Reidel. pp. 2.
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  3. Generalized Measure Theory.Stanley Gudder - 1973 - Foundations of Physics 3 (3):399-411.
    It is argued that a reformulation of classical measure theory is necessary if the theory is to accurately describe measurements of physical phenomena. The postulates of a generalized measure theory are given and the fundamentals of this theory are developed, and the reader is introduced to some open questions and possible applications. Specifically, generalized measure spaces and integration theory are considered, the partial order structure is studied, and applications to hidden variables and the logic of quantum mechanics are given.
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  4.  19
    Realism in Quantum Mechanics.Stanley Gudder - 1989 - Foundations of Physics 19 (8):949-970.
    We first present a realistic framework for quantum probability theory based on the path integral formalism of quantum mechanics and illustrate this framework by constructing a model that describes a quantum particle evolving in a discrete space-time lattice. We then present a finite model for describing the internal dynamics of “elementary particles” and show that this model gives the standard particle classification scheme and successfully predicts particle masses.
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  5.  50
    Quantum Probability and Operational Statistics.Stanley Gudder - 1990 - Foundations of Physics 20 (5):499-527.
    We develop the concept of quantum probability based on ideas of R. Feynman. The general guidelines of quantum probability are translated into rigorous mathematical definitions. We then compare the resulting framework with that of operational statistics. We discuss various relationship between measurements and define quantum stochastic processes. It is shown that quantum probability includes both conventional probability theory and traditional quantum mechanics. Discrete quantum systems, transition amplitudes, and discrete Feynman amplitudes are treated. We close with some examples that illustrate previously (...)
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  6.  10
    A Logical Explanation for Quarks.Stanley P. Gudder - 1982 - Foundations of Physics 12 (4):419-431.
    We construct a quantum logic which generates the usual quark states. It follows from this model that quarks can combine only in quark-antiquark pairs and quark (and antiquark) triples. The ground meson and baryon states are also generated and gluons are discussed.
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  7. D-Algebras.Stanley Gudder - 1996 - Foundations of Physics 26 (6):813-822.
    A D-algebra is a generalization of a D-poset in which a partial order is not assumed. However, if a D-algebra is equipped with a natural partial order, then it becomes a D-poset. It is shown that D-algebras and effect algebras are equivalent algebraic structures. This places the partial operation ⊝ for a D-algebra on an equal footing with the partial operation ⊕ for an effect algebra. An axiomatic structure called an effect stale-space is introduced. Such spaces provide an operational interpretation (...)
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  8. Effect Test Spaces and Effect Algebras.Stanley Gudder - 1997 - Foundations of Physics 27 (2):287-304.
    The concept of an effect test space, which is equivalent to a D-test space of Dvurečenskij and Pulmannová, is introduced. Connections between effect test space. (E-test space, for short) morphisms, and event-morphisms as well as between algebraic E-test spaces and effect algebras, are studied. Bimorphisms and E-test space tensor products are considered. It is shown that any E-test space admits a unique (up to an isomorphism) universal group and that this group, considered as a test group, determines the E-test space (...)
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  9.  77
    Book Review: By Michael A. Nielsen and Isaac L. Chuang. Cambridge University Press, Cambridge, United Kingdom, 2000, I–Xxv+ 676 Pp., $42.00 (Hardcover). [REVIEW]Stanley P. Gudder - 2001 - Foundations of Physics 31 (11):1665-1667.
  10.  14
    Fuzzy Amplitude Densities and Stochastic Quantum Mechanics.Stanley Gudder - 1989 - Foundations of Physics 19 (3):293-317.
    Fuzzy amplitude densities are employed to obtain probability distributions for measurements that are not perfectly accurate. The resulting quantum probability theory is motivated by the path integral formalism for quantum mechanics. Measurements that are covariant relative to a symmetry group are considered. It is shown that the theory includes traditional as well as stochastic quantum mechanics.
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  11.  52
    Basic Properties of Quantum Automata.Stanley Gudder - 2000 - Foundations of Physics 30 (2):301-319.
    This paper develops a theory of quantum automata and their slightly more general versions, q-automata. Quantum languages and η-quantum languages, 0≤η<1, are studied. Functions that can be realized as probability maps for q-automata are characterized. Quantum grammars are discussed and it is shown that quantum languages are precisely those languages that are induced by a quantum grammar. A quantum pumping lemma is employed to show that there are regular languages that are not η-quantum, 0≤η<1.
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  12.  42
    Book Review: New Trends in Quantum Structures. Anatolij Dvurečenskij and Sylvia Pulmannová. Kluwer Academic Publishers, Dordrecht, 2000, I-Xvi, 1-541, $185 (Hardcover). [REVIEW]Stanley P. Gudder - 2001 - Foundations of Physics 31 (5):863-865.
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  13.  37
    Book Review: Quantum Computing and Quantum Communications, Edited by Colin P. Williams. [REVIEW]Stanley P. Gudder - 1999 - Foundations of Physics 29 (10):1639-1642.
  14.  35
    Book Review: Quantum Computation and Quantum Information. By Michael A. Nielsen and Isaac L. Chuang. Cambridge University Press, Cambridge, United Kingdom, 2000, I–Xxv+676 Pp., $42.00 (Hardcover). [REVIEW]Stanley P. Gudder - 2001 - Foundations of Physics 31 (11):1665-1667.
  15.  35
    Realistic Spin.Stanley Gudder - 1992 - Foundations of Physics 22 (1):107-120.
    We present a realistic model in which spin measurements are represented by functions. By employing a simple amplitude density, we derive the usual spin distributions and matrices for the spin-1/2 case. The spin-1 case is also considered. Moreover, we derive the amplitude density itself from deeper principles involving a real-valued influence function.
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  16.  33
    Quantum Stochastic Processes.Stanley Gudder - 1990 - Foundations of Physics 20 (11):1345-1363.
    We first define a class of processes which we call regular quantum Markov processes. We next prove some basic results concerning such processes. A method is given for constructing quantum Markov processes using transition amplitude kernels. Finally we show that the Feynman path integral formalism can be clarified by approximating it with a quantum stochastic process.
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  17.  32
    Perspectives on Quantum Reality: Non-Relativistic, Relativistic, and Field Theoretic: Edited by R. Clifton. Kluwer Academic Publishers, Dordrecht, The Netherlands, Xi+243 Pp. ISBN 0-7923-3812-X. [REVIEW]Stanley Gudder - 1997 - Foundations of Physics 27 (4):605-606.
  18.  13
    Contexts in Quantum Measurement Theory.Stanley Gudder - 2019 - Foundations of Physics 49 (6):647-662.
    State transformations in quantum mechanics are described by completely positive maps which are constructed from quantum channels. We call a finest sharp quantum channel a context. The result of a measurement depends on the context under which it is performed. Each context provides a viewpoint of the quantum system being measured. This gives only a partial picture of the system which may be distorted and in order to obtain a total accurate picture, various contexts need to be employed. We first (...)
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  19.  29
    Bayes' Rule and Hidden Variables.Stanley Gudder & Thomas Armstrong - 1985 - Foundations of Physics 15 (10):1009-1017.
    We show that a quantum system admits hidden variables if and only if there is a rich set of states which satisfy a Bayesian rule. The result is proved using a relationship between Bayesian type states and dispersion-free states. Various examples are presented. In particular, it is shown that for classical systems every state is Bayesian and for traditional Hilbert space quantum systems no state is Bayesian.
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  20. Reality, Locality, and Probability.Stanley P. Gudder - 1984 - Foundations of Physics 14 (10):997-1010.
    It is frequently argued that reality and locality are incompatible with the predictions of quantum mechanics. Various investigators have used this as evidence for the existence of hidden variables. However, Bell's inequalities seem to refute this possibility. Since the above arguments are made within the framework of conventional probability theory, we contend that an alternative solution can be found by an extension of this theory. Elaborating on some ideas of I. Pitowski, we show that within the framework of a generalized (...)
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  21.  26
    Universal Groups of Effect Spaces.Stanley Gudder - 1999 - Foundations of Physics 29 (3):409-422.
    Various axiomatic models for unsharp quantum measurements are investigated. These include effect spaces (E-spaces), effect test spaces (E-test spaces), effect algebras, and test groups. It is shown that a test group G is the universal group of an E-test space if and only if G is strongly atomistic. It follows that if G is strongly atomistic, then G is an interpolation group. We then demonstrate that if G is an interpolation group, then G is the universal group of an E-space. (...)
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  22.  21
    Toward a Rigorous Quantum Field Theory.Stanley Gudder - 1994 - Foundations of Physics 24 (9):1205-1225.
    This paper outlines a framework that may provide a mathematically rigorous quantum field theory. The framework relies upon the methods of nonstandard analysis. A theory of nonstandard inner product spaces and operators on these spaces is first developed. This theory is then applied to construct nonstandard Fock spaces which extend the standard Fock spaces. Then a rigorous framework for the field operators of quantum field theory is presented. The results are illustrated for the case of Klein-Gordon fields.
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  23.  57
    Quantum Graphic Dynamics.Stanley P. Gudder - 1988 - Foundations of Physics 18 (7):751-776.
    A discrete quantum mechanics is developed and used to construct models for discrete space-time and for the internal dynamics of elementary particles. This dynamics is given in terms of particles performing a quantum random walk on a multigraph.
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  24.  14
    Book Review: Quantum Logic in Algebraic Approach, by Milklós Rédei. [REVIEW]Stanley P. Gudder - 1998 - Foundations of Physics 28 (11):1729-1730.
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  25.  28
    The Wave-Particle Dualism: A Tribute to Louis de Broglie on His 90th Birthday. S. Diner, D. Fargue, G. Lochak, F. Selleri.Stanley P. Gudder - 1985 - Philosophy of Science 52 (1):169-170.
  26.  9
    Observables, Calibration, and Effect Algebras.David J. Foulis & Stanley P. Gudder - 2001 - Foundations of Physics 31 (11):1515-1544.
    We introduce and study the D-model, which reflects the simplest situation in which one wants to calibrate an observable. We discuss the question of representing the statistics of the D-model in the context of an effect algebra.
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  27.  8
    Linearity of Expectation Functionals.Stanley P. Gudder - 1985 - Foundations of Physics 15 (1):101-111.
    LetB be the set of bounded observables on a quantum logic. A mapJ: B →R is called an expectation functional ifJ is normalized, positive, continuous, and compatibly linear. Two questions are considered. IsJ linear, and isJ an expectation relative to some state? It is shown that the answers are affirmative for hidden variable logics and most Hilbert space logics. An example is given which shows thatJ can be nonlinear on an arbitrary quantum logic.
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  28.  36
    Quantum Stochastic Models.Stanley Gudder - 1992 - Foundations of Physics 22 (6):839-852.
    Quantum stochastic models are developed within the framework of a measure entity. An entity is a structure that describes the tests and states of a physical system. A measure entity endows each test with a measure and equips certain sets of states as measurable spaces. A stochastic model consists of measurable realvalued function on the set of states, called a generalized action, together with measures on the measurable state spaces. This structure is then employed to compute quantum probabilities of test (...)
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  29.  6
    An Approach to Measurement.Stanley P. Gudder - 1983 - Foundations of Physics 13 (1):35-49.
    We present a new approach to measurement theory. Our definition of measurement is motivated by direct laboratory procedures as they are carried out in practice. The theory is developed within the quantum logic framework. This work clarifies an important problem in the quantum logic approach; namely, where the Hilbert space comes from. We consider the relationship between measurements and observables, and present a Hilbert space embedding theorem. We conclude with a discussion of charge systems.
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  30.  26
    Algebraic Structures Arising in Axiomatic Unsharp Quantum Physics.Gianpiero Cattaneo & Stanley Gudder - 1999 - Foundations of Physics 29 (10):1607-1637.
    This article presents and compares various algebraic structures that arise in axiomatic unsharp quantum physics. We begin by stating some basic principles that such an algebraic structure should encompass. Following G. Mackey and G. Ludwig, we first consider a minimal state-effect-probability (minimal SEFP) structure. In order to include partial operations of sum and difference, an additional axiom is postulated and a SEFP structure is obtained. It is then shown that a SEFP structure is equivalent to an effect algebra with an (...)
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  31.  16
    Survey of a Quark Model.Stanley P. Gudder - 1982 - Foundations of Physics 12 (11):1041-1055.
    We present a survey of a finite-dimensional quark model. We begin with a discussion of measurements on a quantum logic. After making the fundamental assumption that there are three basic colors, the measurement theory provides a natural embedding of the quantum logic into a finite-dimensional Hilbert space. This Hilbert space represents the space of pure quark states. Finite-dimensional quantum mechanics is discussed and the color, and flavor observables are derived. Quark and baryon Hamiltonians are proposed, and a brief description of (...)
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