In this work we will consider systems that are constructed according to
the postulates of classical mechanics, but are modeled by means of
mathematical descriptions that simulate quantum properties. We will call
these systems ‘Quantum Models of Classical Systems’ (QMCS). They can be
used to reproduce interference phenomena and other quantum features such
as entanglement and contextuality. We will focus in the “elastic band
model” (EBM), which depends on a continuous parameter: in this model the
probabilities are non-Kolmogorovian, and the quantum to classical
transition depends on the value of the parameter (Aerts 1998). We will
also discuss recent experiments based on the study of non-coalescent
liquid droplets coupled to pilot waves in the surface of a vibrating
liquid (Couder et. al. 2005, Couder and Fort 2006).
The aim of this article is to study the role of the MCSCs in quantum
information theory (Nielsen and Chuang 2000) from an ontological
perspective. In particular, we will address the following question: how
necessary are quantum systems in order to reproduce the main features of
what is called quantum information theory? We will tackle the task by
analyzing several examples of QMCS and their capability of reproducing
quantum information protocols.
Aerts, D. (1998). “The hidden measurement formalism: what can be
explained and where quantum paradoxes remain.” International Journal of
Theoretical Physics, 37: 291-304.
Couder. Y. and Fort, E. (2006). “Single-particle diffraction and
interference at a macroscopic scale.” Physical Review Letters, 97:
Couder. Y., Fort, E., Gautier, C. and Boudaoud, A. (2005). “From
bouncing to floating: noncoalescence of drops on a fluid bath.” Physical
Review Letters, 94: 177801.
Nielsen, M.A. and Chuang I.L. (2000). Quantum Computation and Quantum
Information. Cambridge: Cambridge University Press.