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Quantum Kaleidoscopes and Bell's theorem P.K.Aravind
 

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 Bell-Kochen-Specker (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 15-observable kaleidoscope, a 24-state kaleidoscope and a 60-state 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 60-state 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.
2

  

Source: Aravind, Padmanabhan K. - Department of Physics, Worcester Polytechnic Institute

 

Collections: Physics