Dimension of physical systems, information processing, and thermodynamics

Nicolas Brunner, Marc Kaplan, Anthony Leverrier, Paul Skrzypczyk

Research output: Contribution to journalArticle (Academic Journal)peer-review

20 Citations (Scopus)


We ask how quantum theory compares to more general physical theories from the point of view of dimension. To do so, we first give two model-independent definitions of the dimension of physical systems, based on measurements and the capacity of storing information. While both definitions are equivalent in classical and quantum mechanics, they are different in generalized probabilistic theories. We discuss in detail the case of a theory known as 'boxworld', and show that such a theory features systems with dimension mismatch. This dimension mismatch can be made arbitrarily large using an amplification procedure. Furthermore, we show that the dimension mismatch of boxworld has strong consequences on its power for performing information-theoretic tasks, leading to the collapse of communication complexity and to the violation of information causality. Finally, we discuss the consequences of a dimension mismatch from the perspective of thermodynamics, and ask whether this effect could break Landauers erasure principle and thus the second law.

Original languageEnglish
Article number123050
JournalNew Journal of Physics
Publication statusPublished - 17 Dec 2014


  • foundations of quantum theory
  • generalized theories
  • information processing


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