dorsal/arxiv
View SchemaQuantum Kaleidoscopes and Bell's theorem
| Authors | P. K. Aravind |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0508130 |
| URL | https://arxiv.org/abs/quant-ph/0508130 |
| DOI | 10.1142/S0217979206034248 |
| Journal | Int. J. Mod. Phys. B 20, 1711-1729 (2006). |
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 Reye's 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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"abstract": "A quantum kaleidoscope is defined as a set of observables, or states,\nconsisting of many different subsets that provide closely related proofs of the\nBell-Kochen-Specker (BKS) and Bell nonlocality theorems. The kaleidoscopes\nprove the BKS theorem through a simple parity argument, which also doubles as a\nproof of Bell\u0027s nonlocality theorem if use is made of the right sort of\nentanglement. Three closely related kaleidoscopes are introduced and discussed\nin this paper: a 15-observable kaleidoscope, a 24-state kaleidoscope and a\n60-state kaleidoscope. The close relationship of these kaleidoscopes to a\nconfiguration of 12 points and 16 lines known as Reye\u0027s configuration is\npointed out. The \"rotations\" needed to make each kaleidoscope yield all its\napparitions are laid out. The 60-state kaleidoscope, whose underlying\ngeometrical structure is that of ten interlinked Reye\u0027s configurations\n(together with their duals), possesses a total of 1120 apparitions that provide\nproofs of the two Bell theorems. Some applications of these kaleidoscopes to\nproblems in quantum tomography and quantum state estimation are discussed.",
"arxiv_id": "quant-ph/0508130",
"authors": [
"P. K. Aravind"
],
"categories": [
"quant-ph"
],
"doi": "10.1142/S0217979206034248",
"journal_ref": "Int. J. Mod. Phys. B 20, 1711-1729 (2006).",
"title": "Quantum Kaleidoscopes and Bell\u0027s theorem",
"url": "https://arxiv.org/abs/quant-ph/0508130"
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