Entanglement and the three-dimensionality of the Bloch ball

Journal Article · Mon Dec 15 04:00:00 EST 2014 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4903510· OSTI ID:22403067

Müller, M. P. ^[1]; Pérez-García, D. ^[2]; Augusiak, R. ^[3]

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1. Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 19, D-69120 Heidelberg (Germany)
2. Departamento de Analisis Matematico and IMI, Universidad Complutense de Madrid, 28040 Madrid (Spain)
3. ICFO-Institut de Ciencies Fotoniques, 08860 Castelldefels, Barcelona (Spain)

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.

• OSTI ID: 22403067
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 12 Vol. 55; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
EUCLIDEAN SPACE
QUANTUM ENTANGLEMENT
QUANTUM MECHANICS
QUANTUM STATES
SPHERES