Classical Models Of Quantum Information

Introduction The past decades have seen an impressive development of quantum information theory (see, e.g., Bennett 1995; Nielsen and Chuang 2010). While the construction of quantum computers remains challenging (Di Vicenzo 1995; Steane 1998; Deutsch and Ekert 2000), other important advances have been achieved (Carolan et al. 2015). Furthermore, new technologies have been applied in communicational security, and many quantum information protocols have been reproduced in the lab. But besides the technological innovations and promises, the development of quantum information techniques has given rise to a (maybe unexpected) rebirth of deep foundational questions (see, e.g., Clifton et al. 2003; Amaral et al. 2014; Popescu 2014). The foundations of quantum mechanics are now seen in a new light. And a new language is used to interrogate our universe, which supplies us knowledge about what nature allows us to do and what not with regard to the transmission and processing of information. What are the physical limits for the transmission of information? Which is the role played by locality and no-signaling conditions in this scenario? What can be computed and what cannot by appealing to realistic physical devices? These are the kind of questions researchers have been wondering, and it turned out that the task of answering them is not trivial at all (see, e.g., Steane 1998; Deutsch and Ekert 2000; Brunner et al. 2014; Popescu 2014). In this setting, the quest for the fundamental principles that specify quantum correlations among other possibilities has played a central role (Popescu 2014). This quest led, for example, to the formulation of the Information Causality Principle (Barnum et al. 2010) and the Exclusivity Principle (Gühne et al. 2010; Amaral et al. 2014; Cabello 2014), among others (Clifton et al. 2003; Oas and de Barros 2015). While there has been an impressive development on the technical side, many debates remain about the meaning of the informational approach for the foundations of quantum mechanics. Specifically: what is quantum information? Can we give a coherent meaning to such a notion? These questions, and even the physical status of the very notion of " quantum information,” have been largely debated (see Lombardi et al. 2016a, and references therein).