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Discretization of the Bloch sphere, fractal invariant sets and Bell's theorem.

Abstract:

An arbitrarily dense discretization of the Bloch sphere of complex Hilbert states is constructed, where points correspond to bit strings of fixed finite length. Number-theoretic properties of trigonometric functions (not part of the quantum-theoretic canon) are used to show that this constructive discretized representation incorporates many of the defining characteristics of quantum systems: completementarity, uncertainty relationships and (with a simple Cartesian product of discretized spher...

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Publication status:
Published
Peer review status:
Peer reviewed

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Institution:
University of Oxford
Division:
MPLS
Department:
Physics
Sub department:
Atmos Ocean & Planet Physics
Role:
Author
ORCID:
0000-0002-7121-2196
Publisher:
The Royal Society
Journal:
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences More from this journal
Volume:
476
Issue:
2236
Article number:
20190350
Publication date:
2020-04-15
Acceptance date:
2020-03-04
DOI:
EISSN:
1471-2946
ISSN:
1364-5021
Pmid:
32398925
Language:
English
Keywords:
Pubs id:
1102776
Local pid:
pubs:1102776
Deposit date:
2020-07-24

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