About the concept of quantum information

S. FORTIN; O. LOMBARDI

San Pablo

Workshop; South American Workshop on the Foundations of Quantum Theory and Cosmology; 2014

International Centre for Theoretical Physics (ICTP)

The word ?information? refers to a polysemantic concept associated with very different phenomena, such as communication, knowledge, reference and meaning. In the discussions about this matter, the first distinction to be introduced is that between a semantic view, according to which information carries semantic content and, thus, is related to notions as reference and meaning, and a statistical view, concerned with the statistical properties of a system and/or the correlations between the states of two systems. Although the locus classicus of the statistical concept is the famous 1948 article by Claude Shannon, there are many other formal concepts of information, such as Fisher information, or algorithmic information. However, even when the attention is restricted to a single formal concept, the problems of interpretation do not disappear.During the last decades, new interpretive problems have arisen with the advent of quantum information, which combine the difficulties in the understanding of the concept of information with the well-known foundational puzzles derived from quantum mechanics itself. This situation contrasts with the huge development of the research field named ?quantum information?, where new formal results multiply rapidly. In this context, the question about the interpretation of quantum information is still far from having an answer on which the whole quantum information community agrees. In fact, the positions about the matter range from those who seem to deny the existence of quantum information, those who consider that it refers to information when it is encoded in quantum systems, and those who conceive it as a new kid of information absolutely different than Shannon information.In the present work we will address the question ?What is quantum information?? from a conceptual viewpoint. For this purpose, first Schumacher?s formalism will be introduced by contrast with Shannon?s theory, and the definition of quantum information in terms of a quantum source will be discussed. Then, the definition of information in terms of coding theorems will be analyzed. These tasks lead us to focus on the relationship between Shannon entropy and von Neumann entropy, and to discuss the differences between the concepts of bit and qubit. In the light of these arguments, we will endow the phenomenon of teleportation with a reading different than usual. Finally, on the basis of the previous discussions, we will analyze the different interpretations of the concept of information, in the search of a characterization adequate both to Shannon?s and Schumacher?s formalisms.