Classical Models for Quantum Information

Abstract

In this chapter, we will discuss the ontological status of the notion of quantuminformation. In the first part, we review the mathematical framework ofa generalized information theory. In this framework, probability theory will play a central role and, thus, we will devote Section 2 to it.We argue that the existence of probabilistic models that go beyond the classical and quantum realms, and the possibility of performing informational protocols in those models, allow us to claim that a generalized information theory can be conceived. Notice that this perspective is complementary to that of other research programs (see, e.g., Holik et al. 2015; Holik et al. 2016, and references therein). In the second part, we will consider the question about the ontology of the possible models satisfying the different instances of that generalized formalism. This will be the content of Section 3. Specifically, we want to study the role quantum mechanics plays in quantum information protocols; the question is whether there are other possible ontologies that can perform the same tasks. We will relate this problem to the existence of many examples of physical systems that are actually constructed using an essentially classical ontology but, on the other hand, are modeled by structures resembling the laws of quantum mechanics (e.g. Aerts 1998; Kwiat et al. 2000; Spreeuw 2001;Couder et al. 2005; Couder and Fort 2006; Qian et al. 2015). Their significancefor us relies in the fact that they can be used to perform quantum information protocols (though, in an inefficient way) (Man?ko et al. 2001; Bhattacharya et al. 2002; Francisco et al. 2006a, 2006b; Francisco and Ledesma 2008; Goldin et al. 2010). On this basis, we will explore the ontological implications of the existence of these simulations. Finally, in Section 4 we will draw our conclusions.