5 found
  1. Subjective probability and quantum certainty.Carlton M. Caves, Christopher A. Fuchs & Rüdiger Schack - 2007 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 38 (2):255-274.
    In the Bayesian approach to quantum mechanics, probabilities—and thus quantum states—represent an agent’s degrees of belief, rather than corresponding to objective properties of physical systems. In this paper we investigate the concept of certainty in quantum mechanics. Particularly, we show how the probability-1 predictions derived from pure quantum states highlight a fundamental difference between our Bayesian approach, on the one hand, and Copenhagen and similar interpretations on the other. We first review the main arguments for the general claim that probabilities (...)
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    Gleason-Type Derivations of the Quantum Probability Rule for Generalized Measurements.Carlton M. Caves, Christopher A. Fuchs, Kiran K. Manne & Joseph M. Renes - 2004 - Foundations of Physics 34 (2):193-209.
    We prove a Gleason-type theorem for the quantum probability rule using frame functions defined on positive-operator-valued measures, as opposed to the restricted class of orthogonal projection-valued measures used in the original theorem. The advantage of this method is that it works for two-dimensional quantum systems and even for vector spaces over rational fields—settings where the standard theorem fails. Furthermore, unlike the method necessary for proving the original result, the present one is rather elementary. In the case of a qubit, we (...)
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    Unpredictability, information, and chaos.Carlton M. Caves & R.�Diger Schack - 1997 - Complexity 3 (1):46-57.
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    Minimal Informationally Complete Measurements for Pure States.Steven T. Flammia, Andrew Silberfarb & Carlton M. Caves - 2005 - Foundations of Physics 35 (12):1985-2006.
    We consider measurements, described by a positive-operator-valued measure (POVM), whose outcome probabilities determine an arbitrary pure state of a D-dimensional quantum system. We call such a measurement a pure-state informationally complete (PS I-complete) POVM. We show that a measurement with 2D−1 outcomes cannot be PS I-complete, and then we construct a POVM with 2D outcomes that suffices, thus showing that a minimal PS I-complete POVM has 2D outcomes. We also consider PS I-complete POVMs that have only rank-one POVM elements and (...)
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    Climbing Mount Scalable: Physical Resource Requirements for a Scalable Quantum Computer. [REVIEW]Robin Blume-Kohout, Carlton M. Caves & Ivan H. Deutsch - 2002 - Foundations of Physics 32 (11):1641-1670.
    The primary resource for quantum computation is Hilbert-space dimension. Whereas Hilbert space itself is an abstract construction, the number of dimensions available to a system is a physical quantity that requires physical resources. Avoiding a demand for an exponential amount of these resources places a fundamental constraint on the systems that are suitable for scalable quantum computation. To be scalable, the effective number of degrees of freedom in the computer must grow nearly linearly with the number of qubits in an (...)
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