Classical models of quantum systems and quantum information
FEDERICO HOLIK AND LEONARDO VANNI
CONICET, University of Buenos Aires (Argentina)
 
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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.

References
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: 154101.
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.