1,128 research outputs found
Ultraproduct for Quantum Structures
Quantum Kripke frames are certain quantum structures recently introduced by Zhong. He has defined certain properties such as Existence of Approximation and Superposition for these structures. In this paper, we define the ultraproduct for the family of quantum Kripke frames and show that the aforementioned properties are invariant under ultraproduct. In this way we prove that the ultraproduct of each family of quantum Kripke frames is also a quantum Kripke frame. We also show the same results for other related quantum structures
Modal quantum theory
We present a discrete model theory similar in structure to ordinary quantum
mechanics, but based on a finite field instead of complex amplitudes. The
interpretation of this theory involves only the "modal" concepts of possibility
and necessity rather than quantitative probability measures. Despite its
simplicity, our model theory includes entangled states and has versions of both
Bell's theorem and the no cloning theorem.Comment: Presented at the 7th Workshop on Quantum Physics and Logic, Oxford
University (29-30 May 2010). Revised 1 Aug 2011 in response to referee
comment
Consistent histories and relativistic invariance in the modal interpretation of quantum mechanics
Modal interpretations of quantum mechanics assign definite properties to
physical systems and specify single-time joint probabilities of these
properties. We show that a natural extension, applying to properties at several
times, can be given if a decoherence condition is satisfied. This extension
defines "consistent histories" of modal properties. We suggest a new form of
the modal scheme, that offers prospects of a more general applicability of the
histories concept. Finally, we discuss a possible way of applying these ideas
to relativistic quantum field theory.Comment: 13 pages, no figure
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