Pentagrams and paradoxes

Abstract

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.

14 pages, 4 figures

References in corpus (9)

• A simple test for hidden variables in spin-1 system
• Experimentally testable state-independent quantum contextuality
• State-independent experimental test of quantum contextuality
• Experimental test of quantum contextuality in neutron interferometry
• State-independent quantum contextuality with single photons
• Quantum advantages in classically defined tasks
• Contextuality and nonlocality in 'no signaling' theories
• `Classical' quantum states
• Dynamic symmetry approach to entanglement

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