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 assumptio...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
16 December 2014
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| In: |
Journal of mathematical physics
Year: 2014, Volume: 55, Issue: 12 |
| ISSN: | 1089-7658 |
| DOI: | 10.1063/1.4903510 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1063/1.4903510 Verlag, lizenzpflichtig, Volltext: https://aip.scitation.org/doi/10.1063/1.4903510 
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| Author Notes: | Ll. Masanes, M.P. Müller, D. Pérez-García, and R. Augusiak |
| Summary: | 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. |
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| Item Description: | Gesehen am 28.10.2020 |
| Physical Description: | Online Resource |
| ISSN: | 1089-7658 |
| DOI: | 10.1063/1.4903510 |