Switch to: References

Add citations

You must login to add citations.
  1. Higher-Order Interference in Extensions of Quantum Theory.Ciarán M. Lee & John H. Selby - 2017 - Foundations of Physics 47 (1):89-112.
    Quantum interference, manifest in the two slit experiment, lies at the heart of several quantum computational speed-ups and provides a striking example of a quantum phenomenon with no classical counterpart. An intriguing feature of quantum interference arises in a variant of the standard two slit experiment, in which there are three, rather than two, slits. The interference pattern in this set-up can be written in terms of the two and one slit patterns obtained by blocking one, or more, of the (...)
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  • Interferometric Computation Beyond Quantum Theory.Andrew J. P. Garner - 2018 - Foundations of Physics 48 (8):886-909.
    There are quantum solutions for computational problems that make use of interference at some stage in the algorithm. These stages can be mapped into the physical setting of a single particle travelling through a many-armed interferometer. There has been recent foundational interest in theories beyond quantum theory. Here, we present a generalized formulation of computation in the context of a many-armed interferometer, and explore how theories can differ from quantum theory and still perform distributed calculations in this set-up. We shall (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  • Oracles and Query Lower Bounds in Generalised Probabilistic Theories.Howard Barnum, Ciarán M. Lee & John H. Selby - 2018 - Foundations of Physics 48 (8):954-981.
    We investigate the connection between interference and computational power within the operationally defined framework of generalised probabilistic theories. To compare the computational abilities of different theories within this framework we show that any theory satisfying four natural physical principles possess a well-defined oracle model. Indeed, we prove a subroutine theorem for oracles in such theories which is a necessary condition for the oracle model to be well-defined. The four principles are: causality, purification, strong symmetry, and informationally consistent composition. Sorkin has (...)
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark  
  • On Defining the Hamiltonian Beyond Quantum Theory.Dominic Branford, Oscar C. O. Dahlsten & Andrew J. P. Garner - 2018 - Foundations of Physics 48 (8):982-1006.
    Energy is a crucial concept within classical and quantum physics. An essential tool to quantify energy is the Hamiltonian. Here, we consider how to define a Hamiltonian in general probabilistic theories—a framework in which quantum theory is a special case. We list desiderata which the definition should meet. For 3-dimensional systems, we provide a fully-defined recipe which satisfies these desiderata. We discuss the higher dimensional case where some freedom of choice is left remaining. We apply the definition to example toy (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark  
  • Testing Born’s Rule in Quantum Mechanics for Three Mutually Exclusive Events.Immo Söllner, Benjamin Gschösser, Patrick Mai, Benedikt Pressl, Zoltán Vörös & Gregor Weihs - 2012 - Foundations of Physics 42 (6):742-751.
    We present a new experimental approach using a three-path interferometer and find a tighter empirical upper bound on possible violations of Born’s Rule. A deviation from Born’s rule would result in multi-order interference. Among the potential systematic errors that could lead to an apparent violation we specifically study the nonlinear response of our detectors and present ways to calibrate this error in order to obtain an even better bound.
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark  
  • Three-Slit Experiments and Quantum Nonlocality.Gerd Niestegge - 2013 - Foundations of Physics 43 (6):805-812.
    An interesting link between two very different physical aspects of quantum mechanics is revealed; these are the absence of third-order interference and Tsirelson’s bound for the nonlocal correlations. Considering multiple-slit experiments—not only the traditional configuration with two slits, but also configurations with three and more slits—Sorkin detected that third-order (and higher-order) interference is not possible in quantum mechanics. The EPR experiments show that quantum mechanics involves nonlocal correlations which are demonstrated in a violation of the Bell or CHSH inequality, but (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  • A Generalized Quantum Theory.Gerd Niestegge - 2014 - Foundations of Physics 44 (11):1216-1229.
    In quantum mechanics, the selfadjoint Hilbert space operators play a triple role as observables, generators of the dynamical groups and statistical operators defining the mixed states. One might expect that this is typical of Hilbert space quantum mechanics, but it is not. The same triple role occurs for the elements of a certain ordered Banach space in a much more general theory based upon quantum logics and a conditional probability calculus (which is a quantum logical model of the Lüders-von Neumann (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   2 citations