The Ontological Status Of Quantum Information

Matteo Morganti

Nick Wiggershaus

While the inclusion of information theoretical concepts into (quantum)\nphysics has shown enormous success in recent years, the ontology of information\nremains puzzling. Therefore, this thesis aims to contribute to\nthe debate about the ontological status of information in physics. Most\nof the recent debates have focused on syntactic information measures\nand especially Shannon Information, a concept originally stemming from\nCommunication Theory. This thesis incorporates another syntactic information\nmeasure, the so far largely underrepresented notion of Algorithmic\nInformation or Kolmogorov Complexity, a concept often applied\nin Computer Science. Shannon Information and Kolmogorov Complexity\nare linked through Coding Theory and have similar characteristics.\nThrough the comparison of Shannon Information and Kolmogorov Complexity\na framework is developed which analyses the respective information\nmeasures in relation to uncertainty and semantic information. In addition,\nthis framework investigates whether information can be regarded\na material entity and examines to what extent information is conventional.\nIt turns out that in the classical case Shannon Information and\nKolmogorov Complexity are both abstract and highly conventional entities,\nwhich must not be confused with uncertainty and do not bear any\nrelations with semantic information. Virtually the same results are obtained\nin the quantum case, save for the high degree of conventionality;\nit is argued that Quantum Theory constrains the conventional choices of\nthose who wish to use either theory.

Chris Timpson

HALİL KEMAL İLTER

Gennaro Auletta, Shang-Yung Wang

In this chapter, we shall collect and generalize the results of the previous three chapters. We shall come back to the issue of quantum correlations in terms of information. We shall consider now the second aspect of quantum information [see Section 11.3], that is, information selection leading to a local growth of entropy (as it is the case during ameasurement). This will be the basis for examining again the whole process of measurement and finally assign an ontological status to fundamental entities of quantum theory like states, observables, and properties.

Federico Holik, G. M. Bosyk

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.