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Title: Entanglement and the three-dimensionality of the Bloch ball

We consider a very natural generalization of quantum theory by letting the dimension of the Bloch ball be not necessarily three. We analyze bipartite state spaces where each of the components has a d-dimensional Euclidean ball as state space. In addition to this, we impose two very natural assumptions: the continuity and reversibility of dynamics and the possibility of characterizing bipartite states by local measurements. We classify all these bipartite state spaces and prove that, except for the quantum two-qubit state space, none of them contains entangled states. Equivalently, in any of these non-quantum theories, interacting dynamics is impossible. This result reveals that “existence of entanglement” is the requirement with minimal logical content which singles out quantum theory from our family of theories.
Authors:
 [1] ;  [2] ;  [3] ;  [4]
  1. Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT (United Kingdom)
  2. Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 19, D-69120 Heidelberg (Germany)
  3. Departamento de Analisis Matematico and IMI, Universidad Complutense de Madrid, 28040 Madrid (Spain)
  4. ICFO-Institut de Ciencies Fotoniques, 08860 Castelldefels, Barcelona (Spain)
Publication Date:
OSTI Identifier:
22403067
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 12; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; EUCLIDEAN SPACE; QUANTUM ENTANGLEMENT; QUANTUM MECHANICS; QUANTUM STATES; SPHERES