Pentagrams and paradoxes

Details Pentagrams and paradoxes Pentagrams and paradoxes

2009-09-25

arxiv.org/abs/0909.4713v1

Found. Phys. vol. 41 p. 41 (2011)

Physics

Quantum Physics

14 pages, 4 figures

Scientific paper

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.

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