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Entanglement and the three-dimensionality of the Bloch ball

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Masanes, Lluís and Müller, M.P. and Pérez García, David and Augusiak, Remigiusz (2014) Entanglement and the three-dimensionality of the Bloch ball. Journal of Mathematical Physics, 55 (12). ISSN 0022-2488

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Official URL: http://scitation.aip.org/content/aip/journal/jmp/55/12/10.1063/1.4903510




Abstract

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 twoqubit 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


Item Type:Article
Uncontrolled Keywords:Quantum-mechanics
Subjects:Sciences > Physics > Mathematical physics
Sciences > Physics > Quantum theory
ID Code:28348
Deposited On:12 Feb 2015 13:40
Last Modified:12 Feb 2015 13:40

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