On properties of Karlsson Hadamards and sets of mutually unbiased bases in dimension six
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...
متن کاملMaximal Sets of Mutually Unbiased Quantum States in Dimension Six
We study sets of pure states in a Hilbert space of dimension d which are mutually unbiased (MU), that is, the moduli of their scalar products are equal to zero, one, or 1/ √ d. These sets will be called a MU constellation, and if four MU bases were to exist for d = 6, they would give rise to 35 different MU constellations. Using a numerical minimisation procedure, we are able to identify only 1...
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 کاملReal Mutually Unbiased Bases
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...
متن کاملConstructions of Mutually Unbiased Bases
Two orthonormal bases B andB′ of a d-dimensional complex inner-product space are called mutually unbiased if and only if |〈b|b〉| = 1/d holds for all b ∈ B and b′ ∈ B′. The size of any set containing pairwise mutually unbiased bases of C cannot exceed d + 1. If d is a power of a prime, then extremal sets containing d+1 mutually unbiased bases are known to exist. We give a simplified proof of thi...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2015
ISSN: 0024-3795
DOI: 10.1016/j.laa.2014.10.017