 
Summary: 1
Quantum Kaleidoscopes and Bell's theorem
P.K.Aravind
Physics Department
Worcester Polytechnic Institute
Worcester, MA 01609
ABSTRACT
A quantum kaleidoscope is defined as a set of observables, or states, consisting of many
different subsets that provide closely related proofs of the BellKochenSpecker (BKS) and Bell
nonlocality theorems. The kaleidoscopes prove the BKS theorem through a simple parity
argument, which also doubles as a proof of Bell's nonlocality theorem if use is made of the right
sort of entanglement. Three closely related kaleidoscopes are introduced and discussed in this
paper: a 15observable kaleidoscope, a 24state kaleidoscope and a 60state kaleidoscope. The
close relationship of these kaleidoscopes to a configuration of 12 points and 16 lines known as
Reye's configuration is pointed out. The "rotations" needed to make each kaleidoscope yield all
its apparitions are laid out. The 60state kaleidoscope, whose underlying geometrical structure is
that of ten interlinked Reyes' configurations (together with their duals), possesses a total of
1120 apparitions that provide proofs of the two Bell theorems. Some applications of these
kaleidoscopes to problems in quantum tomography and quantum state estimation are discussed.
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