1,066 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
A New Relation between post and pre-optimal measurement states
When an optimal measurement is made on a qubit and what we call an Unbiased
Mixture of the resulting ensembles is taken, then the post measurement density
matrix is shown to be related to the pre-measurement density matrix through a
simple and linear relation. It is shown that such a relation holds only when
the measurements are made in Mutually Unbiased Bases- MUB. For Spin-1/2 it is
also shown explicitly that non-orthogonal measurements fail to give such a
linear relation no matter how the ensembles are mixed. The result has been
proved to be true for arbitrary quantum mechanical systems of finite
dimensional Hilbert spaces. The result is true irrespective of whether the
initial state is pure or mixed.Comment: 4 pages in REVTE
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