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  1.  35
    Quantum Mechanics Without Probability Amplitudes.William K. Wootters - 1986 - Foundations of Physics 16 (4):391-405.
    First steps are taken toward a formulation of quantum mechanics which avoids the use of probability amplitudes and is expressed entirely in terms of observable probabilities. Quantum states are represented not by state vectors or density matrices but by “probability tables,” which contain only the probabilities of the outcomes of certain special measurements. The rule for computing transition probabilities, normally given by the squared modulus of the inner product of two state vectors, is re-expressed in terms of probability tables. The (...)
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  2.  64
    Limited Holism and Real-Vector-Space Quantum Theory.Lucien Hardy & William K. Wootters - 2012 - Foundations of Physics 42 (3):454-473.
    Quantum theory has the property of “local tomography”: the state of any composite system can be reconstructed from the statistics of measurements on the individual components. In this respect the holism of quantum theory is limited. We consider in this paper a class of theories more holistic than quantum theory in that they are constrained only by “bilocal tomography”: the state of any composite system is determined by the statistics of measurements on pairs of components. Under a few auxiliary assumptions, (...)
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  3.  39
    Random Quantum States.William K. Wootters - 1990 - Foundations of Physics 20 (11):1365-1378.
    This paper examines the statistical properties of random quantum states, for four different kinds of random state:(1) a pure state chosen at random with respect to the uniform measure on the unit sphere in a finite-dimensional Hilbert space;(2) a random pure state in a real space;(3) a pure state chosen at random except that a certain expectation value is fixed;(4) a random mixed state with fixed eigenvalues. For the first two of these, we give examples of simple states of a (...)
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  4.  29
    Entanglement Sharing in Real-Vector-Space Quantum Theory.William K. Wootters - 2012 - Foundations of Physics 42 (1):19-28.
    The limitation on the sharing of entanglement is a basic feature of quantum theory. For example, if two qubits are completely entangled with each other, neither of them can be at all entangled with any other object. In this paper we show, at least for a certain standard definition of entanglement, that this feature is lost when one replaces the usual complex vector space of quantum states with a real vector space. Moreover, the difference between the two theories is extreme: (...)
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  5.  55
    Why Things Fall.William K. Wootters - 2003 - Foundations of Physics 33 (10):1549-1557.
    Let us accept the quantum mechanical description of a free particle and one fact from special relativity: rest mass contributes to energy. If we add to this bare framework one additional fact—that time runs slower near the earth—we can account for our everyday experience of gravity.
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