134 research outputs found
A discussion on the origin of quantum probabilities
We study the origin of quantum probabilities as arising from non-boolean
propositional-operational structures. We apply the method developed by Cox to
non distributive lattices and develop an alternative formulation of
non-Kolmogorvian probability measures for quantum mechanics. By generalizing
the method presented in previous works, we outline a general framework for the
deduction of probabilities in general propositional structures represented by
lattices (including the non-distributive case).Comment: Improved versio
Pattern Recognition In Non-Kolmogorovian Structures
We present a generalization of the problem of pattern recognition to
arbitrary probabilistic models. This version deals with the problem of
recognizing an individual pattern among a family of different species or
classes of objects which obey probabilistic laws which do not comply with
Kolmogorov's axioms. We show that such a scenario accommodates many important
examples, and in particular, we provide a rigorous definition of the classical
and the quantum pattern recognition problems, respectively. Our framework
allows for the introduction of non-trivial correlations (as entanglement or
discord) between the different species involved, opening the door to a new way
of harnessing these physical resources for solving pattern recognition
problems. Finally, we present some examples and discuss the computational
complexity of the quantum pattern recognition problem, showing that the most
important quantum computation algorithms can be described as non-Kolmogorovian
pattern recognition problems
A discussion on particle number and quantum indistinguishability
The concept of individuality in quantum mechanics shows radical differences
from the concept of individuality in classical physics, as E. Schroedinger
pointed out in the early steps of the theory. Regarding this fact, some authors
suggested that quantum mechanics does not possess its own language, and
therefore, quantum indistinguishability is not incorporated in the theory from
the beginning. Nevertheless, it is possible to represent the idea of quantum
indistinguishability with a first order language using quasiset theory (Q). In
this work, we show that Q cannot capture one of the most important features of
quantum non individuality, which is the fact that there are quantum systems for
which particle number is not well defined. An axiomatic variant of Q, in which
quasicardinal is not a primitive concept (for a kind of quasisets called finite
quasisets), is also given. This result encourages the searching of theories in
which the quasicardinal, being a secondary concept, stands undefined for some
quasisets, besides showing explicitly that in a set theory about collections of
truly indistinguishable entities, the quasicardinal needs not necessarily be a
primitive concept.Comment: 46 pages, no figures. Accepted by Foundations of Physic
Quantal effects and MaxEnt
Convex operational models (COMs) are considered as great extrapolations to
larger settings of any statistical theory. In this article we generalize the
maximum entropy principle (MaxEnt) of Jaynes' to any COM. After expressing
Max-Ent in a geometrical and latttice theoretical setting, we are able to cast
it for any COM. This scope-amplification opens the door to a new
systematization of the principle and sheds light into its geometrical
structure
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