Related papers: Quasi-set theory for bosons and fermions: quantum …
Quasi-set theory provides us a mathematical background for dealing with collections of indistinguishable elementary particles. In this paper, we show how to obtain the usual statistics (Maxwell-Boltzmann, Bose-Einstein, and Fermi-Dirac)…
In this article, we discuss the identity and indistinguishability of quantum systems and the consequent need to introduce an extra postulate in Quantum Mechanics to correctly describe situations involving indistinguishable particles. This…
We have recently showed that it is possible to deal with collections of indistinguishable elementary particles (in the context of quantum mechanics) in a set-theoretical framework by using hidden variables, in a sense. In the present paper…
Quasi-set theory allows us a non trivial relation between indistinguishability and nonlocality into the context of Einstein- Podolsky-Rosen experiment. Quasi-set theory is a set theory which provides a manner for dealing with collections of…
Quasi-set theory is a first order theory without identity, which allows us to cope with non-individuals in a sense. A weaker equivalence relation called ``indistinguishability'' is an extension of identity in the sense that if $x$ is…
This paper proposes groove-like potential structures for the observation of quantum information processing by trapped particles. As an illustration the effect of quantum statistics at a 50-50 beam splitter is investigated. For…
We propose the principle, the law of statistical balance for basic physical observables, which specifies quantum statistical theory among all other statistical theories of measurements. It seems that this principle might play in quantum…
In any given experimental scenario, the rules of quantum theory provide statistical distributions that the observed outcomes are expected to follow. The set formed by all these distributions contains the imprint of quantum theory, capturing…
The aim of the paper is to derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The main extensions, which also can be motivated from an applied statistics point…
Quantum theory has the intriguing feature that is inconsistent with noncontextual hidden variable models, for which the outcome of a measurement does not depend on which other compatible measurements are being performed concurrently. While…
According to Cantor, a set is a collection into a whole of defined and separate (we shall say distinct) objects. So, a natural question is ``How to treat as `sets' collections of indistinguishable objects?". This is the aim of quasi-set…
Quantum matter in three spatial dimensions is observed to consist exclusively of bosons and fermions. Whether this empirical fact follows from basic consistency requirements of quantum theory itself or must be imposed as an additional…
Quantum coherence, a basic feature of quantum mechanics residing in superpositions of quantum states, is a resource for quantum information processing. Coherence emerges in a fundamentally different way for nonidentical and identical…
In this tutorial, we present the definition, interpretation and properties of some of the main quasiprobabilities that can describe the statistics of measurement outcomes evaluated at two or more times. Such statistics incorporate the…
A full treatment for the scattering of an arbitrary number of bosons through a Bell multiport beam splitter is presented that includes all possible output arrangements. Due to exchange symmetry, the event statistics differs dramatically…
We stress the notion of statistical experiment, which is mandatory for quantum mechanics, and recall Ludwig's foundation of quantum mechanics, which provides the most general framework to deal with statistical experiments giving evidence…
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…
Our aim in this paper is to take quite seriously Heinz Post's claim that the non-individuality and the indiscernibility of quantum objects should be introduced right at the start, and not made a posteriori by introducing symmetry…
We discuss a reconstruction of standard quantum mechanics assuming indistinguishability right from the start, by appealing to quasi-set theory. After recalling the fundamental aspects of the construction and introducing some improvements in…
The empirical rule that systems of identical particles always obey either Bose or Fermi statistics is customarily imposed on the theory by adding it to the axioms of nonrelativistic quantum mechanics, with the result that other statistical…