1,672 research outputs found
Conservation of information and the foundations of quantum mechanics
We review a recent approach to the foundations of quantum mechanics inspired
by quantum information theory. The approach is based on a general framework,
which allows one to address a large class of physical theories which share
basic information-theoretic features. We first illustrate two very primitive
features, expressed by the axioms of causality and purity-preservation, which
are satisfied by both classical and quantum theory. We then discuss the axiom
of purification, which expresses a strong version of the Conservation of
Information and captures the core of a vast number of protocols in quantum
information. Purification is a highly non-classical feature and leads directly
to the emergence of entanglement at the purely conceptual level, without any
reference to the superposition principle. Supplemented by a few additional
requirements, satisfied by classical and quantum theory, it provides a complete
axiomatic characterization of quantum theory for finite dimensional systems.Comment: 11 pages, contribution to the Proceedings of the 3rd International
Conference on New Frontiers in Physics, July 28-August 6 2014, Orthodox
Academy of Crete, Kolymbari, Cret
Naming the largest number: Exploring the boundary between mathematics and the philosophy of mathematics
What is the largest number accessible to the human imagination? The question
is neither entirely mathematical nor entirely philosophical. Mathematical
formulations of the problem fall into two classes: those that fail to fully
capture the spirit of the problem, and those that turn it back into a
philosophical problem
Meta SOS - A Maude Based SOS Meta-Theory Framework
Meta SOS is a software framework designed to integrate the results from the
meta-theory of structural operational semantics (SOS). These results include
deriving semantic properties of language constructs just by syntactically
analyzing their rule-based definition, as well as automatically deriving sound
and ground-complete axiomatizations for languages, when considering a notion of
behavioural equivalence. This paper describes the Meta SOS framework by
blending aspects from the meta-theory of SOS, details on their implementation
in Maude, and running examples.Comment: In Proceedings EXPRESS/SOS 2013, arXiv:1307.690
Probabilistic thread algebra
We add probabilistic features to basic thread algebra and its extensions with
thread-service interaction and strategic interleaving. Here, threads represent
the behaviours produced by instruction sequences under execution and services
represent the behaviours exhibited by the components of execution environments
of instruction sequences. In a paper concerned with probabilistic instruction
sequences, we proposed several kinds of probabilistic instructions and gave an
informal explanation for each of them. The probabilistic features added to the
extension of basic thread algebra with thread-service interaction make it
possible to give a formal explanation in terms of non-probabilistic
instructions and probabilistic services. The probabilistic features added to
the extensions of basic thread algebra with strategic interleaving make it
possible to cover strategies corresponding to probabilistic scheduling
algorithms.Comment: 25 pages (arXiv admin note: text overlap with arXiv:1408.2955,
arXiv:1402.4950); some simplifications made; substantially revise
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