King ’ s problem with mutually unbiased bases for arbitrary levels
نویسنده
چکیده
The Mean King’s problem with mutually unbiased bases is reconsidered for arbitrary d-level systems. Hayashi, Horibe and Hashimoto [Phys. Rev. A 71, 052331 (2005)] related the problem to the existence of a maximal set of d − 1 mutually orthogonal Latin squares, in their restricted setting that allows only measurements of projection-valued measures. However, we then cannot find a solution to the problem when e.g., d = 6 or d = 10. In contrast to their result, we show that the King’s problem always has a solution for arbitrary levels if we also allow positive operator-valued measures. In constructing the solution, we use orthogonal arrays in combinatorial design theory.
منابع مشابه
Blind encoding into qudits
We consider the problem of encoding classical information into unknown qudit states belonging to any basis, of a maximal set of mutually unbiased bases, by one party and then decoding by another party who has perfect knowledge of the basis. Working with qudits of prime dimensions, we point out a no-go theorem that forbids shift operations on arbitrary unknown states. We then provide the necessa...
متن کاملSolution to the King’s Problem in Prime Power Dimensions
The King’s Problem [1] is the following: A physicist is trapped on an island ruled by a mean king who promises to set her free if she can give him the answer to the following puzzle. The physicist is asked to prepare a d-state quantum system in any state of her choosing and give it to the king, who measures one of several sets of mutually unbiased observables (this term will be defined below) o...
متن کاملNew construction of mutually unbiased bases in square dimensions
We show that k = w + 2 mutually unbiased bases can be constructed in any square dimension d = s provided that there are w mutually orthogonal Latin squares of order s. The construction combines the design-theoretic objects (k, s)-nets (which can be constructed from w mutually orthogonal Latin squares of order s and vice versa) and generalized Hadamard matrices of size s. Using known lower bound...
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...
متن کاملMutually Unbiased bases: a brief survey
Mutually unbiased bases have important applications in Quantum Computation and more specifically in quantum state determination and quantum key distribution. However these applications rely on the existence of a complete set of such bases. Even though they’re being studied since the 1970’s the problem of finding a complete set of mutually unbiased bases is only solved for dimensions which are a...
متن کامل