Mutually unbiased bases in six dimensions: The four most distant bases
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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We tabulate bounds on the optimal number of mutually unbiased bases in R. For most dimensions d, it can be shown with relatively simple methods that either there are no real orthonormal bases that are mutually unbiased or the optimal number is at most either 2 or 3. We discuss the limitations of these methods when applied to all dimensions, shedding some light on the difficulty of obtaining tig...
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One of the essential features of quantum mechanics is that most pairs of observables cannot be measured simultaneously. This phenomenon manifests itself most strongly when observables are related to mutually unbiased bases. In this paper, we shed some light on the connection between mutually unbiased bases and another essential feature of quantum mechanics, quantum entanglement. It is shown tha...
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All complex Hadamard matrices in dimensions two to five are known. We use this fact to derive all inequivalent sets of mutually unbiased (MU) bases in low dimensions. We find a three-parameter family of triples of MU bases in dimension four and two inequivalent classes of MU triples in dimension five. We confirm that the complete sets of (d+1)MU bases are unique (up to equivalence) in dimension...
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In a complex vector space of dimension N , by a full set of mutually unbiased bases (MUB’s) we mean a set of N+1 orthonormal bases such that the modulus square of the scalar product of any member of one basis with any member of any other basis is equal to 1/N . If we take e to denote the k vector in the α orthonormal basis, then having a full set of MUB’s amounts to having a collection e ; α = ...
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ژورنال
عنوان ژورنال: Physical Review A
سال: 2011
ISSN: 1050-2947,1094-1622
DOI: 10.1103/physreva.83.062303