Maximal orthoplectic fusion frames from mutually unbiased bases and block designs
نویسندگان
چکیده
منابع مشابه
Real 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 کاملOn the Maximal Number of Real Mutually Unbiased Bases
In this note I point out that (1) pairs of real mutually unbiased bases (i.e., orthonormal bases of R) can only exist in dimensions 2 or d where d is a multiple of 4 and that (2) triples of real mutually unbiased bases can only exist in dimensions d that are also squares. For the case d = 2 the maximal number of real MUBs is given by (d+ 2)/2 (this follows from known results on extremal euclide...
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 کاملUnextendibility of Mutually Unbiased Bases
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...
متن کاملEntanglement in mutually unbiased bases
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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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2018
ISSN: 0002-9939,1088-6826
DOI: 10.1090/proc/13956