What is quantum information?

Abstract

The word 'information' refers to a polysemantic concept associated with very different phenomena, such as communication, knowledge, reference and meaning (Floridi 2010(Floridi , 2011. 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, However, the problems of interpretation do not disappear even when the attention is restricted to a single formal concept (see Lombardi, Holik and Vanni 2014).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 'What is 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 (Duwell 2003), those who consider that it refers to information when it is encoded in quantum systems , and those who conceive it as a new kind of information absolutely different than Shannon information (Jozsa 1998;Brukner and Zeilinger 2001).In the present article we will address the question 'What is quantum information?' from a conceptual viewpoint. For this purpose, in Section 2 Schumacher's formalism is introduced by contrast with Shannon's theory. In Section 3 the definition of quantum information in terms of a quantum source is discussed. Section 4 is devoted to analyze the definition of information in terms of coding theorems. These tasks lead us to focus on the relationship between Shannon entropy and von Neumann entropy in Section 5, and to discuss the differences between the concepts of bit and

What is quantum information?

“…Such an objection can succeed only if to be any kind of information it is necessary that different pieces of information are always distinguishable from one another. This is a position that needs to be argued for, but Lombardi et al () do not provide that argumentation.…”

“…Lombardi et al () present several other kinds of objections. One objection is that quantum information is not generally accessible at the destination.…”

“…Fortin and Lombardi () and Lombardi et al () seem to think that the idea of a quantum communication system without a quantum coding process is conceptually problematic. It is not clear why the idea of a quantum information source in absence of coding is problematic, especially when one distinguishes between the qualitative and quantitative concepts of information.…”

“…A question of fundamental interest is: What is quantum information? This question is the focus of a recent edited collection by Lombardi, Fortin, Holik, and López (). In this paper, I will provide the reader with an introduction to some of the issues associated with answering this question.…”

Quantum Information as a Non-Kolmogorovian Generalization of Shannon’s Theory

“…Due to the fact that the final output of the source is now represented by a density matrix ρ = p x ρ x (i.e., by a non-Kolmogorovian measure), then von Neumann's entropy comes onto stage. This is expressed, for example, in Schumacher's quantum coding theorem, in which the optimal bound for coding is expressed in terms of this quantity [114,115].…”