Unbiased bases (Hadamards) for six-level systems: Four ways from Fourier
نویسندگان
چکیده
منابع مشابه
Constructing Mutually Unbiased Bases in Dimension Six
The density matrix of a qudit may be reconstructed with optimal efficiency if the expectation values of a specific set of observables are known. In dimension six, the required observables only exist if it is possible to identify six mutually unbiased complex (6 × 6) Hadamard matrices. Prescribing a first Hadamard matrix, we construct all others mutually unbiased to it, using algebraic computati...
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This is a review of the problem of Mutually Unbiased Bases in finite dimensional Hilbert spaces, real and complex. Also a geometric measure of “mubness” is introduced, and applied to some explicit calculations in six dimensions (partly done by Björck and by Grassl). Although this does not yet solve any problem, some appealing structures emerge. Talk at the Växjö conference on Foundations of Pro...
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In quantum information, complementarity of quantum mechanical observables plays a key role. The eigenstates of two complementary observables form a pair of mutually unbiased bases (MUBs). More generally, a set of MUBs consists of bases that are all pairwise unbiased. Except for specific dimensions of the Hilbert space, the maximal sets of MUBs are unknown in general. Even for a dimension as low...
متن کاملMutually unbiased bases and Hadamard matrices of order six
We report on a search for mutually unbiased bases MUBs in six dimensions. We find only triplets of MUBs, and thus do not come close to the theoretical upper bound 7. However, we point out that the natural habitat for sets of MUBs is the set of all complex Hadamard matrices of the given order, and we introduce a natural notion of distance between bases in Hilbert space. This allows us to draw a ...
متن کاملMubs and Hadamards of Order Six
We report on a search for mutually unbiased bases (MUBs) in 6 dimensions. We find only triplets of MUBs, and thus do not come close to the theoretical upper bound 7. However, we point out that the natural habitat for sets of MUBs is the set of all complex Hadamard matrices of the given order, and we introduce a natural notion of distance between bases in Hilbert space. This allows us to draw a ...
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ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 2009
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.3059166