2,030 research outputs found
Solution to the King's Problem in prime power dimensions
It is shown how to ascertain the values of a complete set of mutually
complementary observables of a prime power degree of freedom by generalizing
the solution in prime dimensions given by Englert and Aharonov [Phys. Lett.
A284, 1-5 (2001)].Comment: 16 pages, 6 tables. A typo in an inequality on the line preceding
Eqn.(4)has been correcte
Quantum Kaleidoscopes and Bell's theorem
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.Comment: Two new references (No. 21 and 22) to related work have been adde
The generalized Kochen-Specker theorem
A proof of the generalized Kochen-Specker theorem in two dimensions due to
Cabello and Nakamura is extended to all higher dimensions. A set of 18 states
in four dimensions is used to give closely related proofs of the generalized
Kochen-Specker, Kochen-Specker and Bell theorems that shed some light on the
relationship between these three theorems.Comment: 5 pages, 1 Table. A new third paragraph and an additional reference
have been adde
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