Entropic bounds for unitary testers and mutually unbiased unitary bases
نویسندگان
چکیده
منابع مشابه
Generation of Mutually Unbiased Bases as Powers of a Unitary Matrix in 2-power Dimensions
Let q be a power of 2. We show by representation theory that there exists a q × q unitary matrix of multiplicative order q + 1 whose powers generate q + 1 complex pairwise mutually unbiased bases in C. When q is a power of an odd prime, there is a q × q unitary matrix of multiplicative order q+1 whose first (q+1)/2 powers generate (q+1)/2 complex pairwise mutually unbiased bases. We also show h...
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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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The construction of unitary operator bases in a finite-dimensional Hilbert space is reviewed through a nonstandard approach combinining angular momentum theory and representation theory of SU(2). A single formula for the bases is obtained from a polar decomposition of SU(2) and analysed in terms of cyclic groups, quadratic Fourier transforms, Hadamard matrices and generalized Gauss sums. Weyl p...
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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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Besides being of independent interest in understanding the structure of (partial) MUB collections and their conjugacy classes, satisfactory answers to these questions will help the following investigations: – the search for lower bounds on the number of MUBs and specifically for efficient constructions; – the search for upper bounds on the number of MUBs even for small non-prime-power dimension...
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ژورنال
عنوان ژورنال: Annals of Physics
سال: 2020
ISSN: 0003-4916
DOI: 10.1016/j.aop.2019.168043