Pentagrams and paradoxes. (English) Zbl 1210.81011
Summary: Klyachko and coworkers consider an orthogonality graph in the form of a pentagram, and, in this way, derive a Kochen-Specker inequality for spin 1 systems. In some low-dimensional situations, Hilbert spaces are naturally organised, by a magical choice of basis, into \(SO(N)\) orbits. Combining these ideas some very elegant results emerge. We give a careful discussion of the pentagram operator, and then show how the pentagram underlies a number of other quantum “paradoxes”, such as that of Hardy.
MSC:
| 81P13 | Contextuality in quantum theory |
| 81P05 | General and philosophical questions in quantum theory |
| 22E70 | Applications of Lie groups to the sciences; explicit representations |
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