Related papers: The problem of mutually unbiased bases in dimensio…
We use difference sets to construct interesting sets of lines in complex space. Using (v,k,1)-difference sets, we obtain k^2-k+1 equiangular lines in C^k when k-1 is a prime power. Using semiregular relative difference sets with parameters…
Lower bounds and impossibility results in distributed computing are both intellectually challenging and practically important. Hundreds if not thousands of proofs appear in the literature, but surprisingly, the vast majority of them apply…
Certifying entanglement is an important step in the development of many quantum technologies, especially for higher-dimensional systems, where entanglement promises increased capabilities for quantum communication and computation. A key…
We provide a construction of sets of (d/2+1) mutually unbiased bases (MUBs) in dimensions d=4,8 using maximal commuting classes of Pauli operators. We show that these incomplete sets cannot be extended further using the operators of the…
We consider a problem of bounding the maximal possible multiplicity of a zero at of some expansions $\sum a_i F_i(x)$, at a certain point $c,$ depending on the chosen family $\{F_i \}$. The most important example is a polynomial with $c=1.$…
Recommender systems are seen as an effective tool to address information overload, but it is widely known that the presence of various biases makes direct training on large-scale observational data result in sub-optimal prediction…
We develop a general distributed implementation of an adaptive fast multipole method in three space dimensions. We rely on a balanced type of adaptive space discretisation which supports a highly transparent and fully distributed…
Studying and understanding social networks is crucial for accurately defining ideological polarization, since they enable precise modeling of social structures. One of the limitations of many methods for quantifying polarization on networks…
Entropic uncertainty relations, based on sums of entropies of probability distributions arising from different measurements on a given pure state, can be seen as a generalization of the Heisenberg uncertainty relation that is in many cases…
Mutually Unbiased Bases (MUBs) constitute a fundamental geometric structure in quantum theory, known for providing an optimal measurement scheme for quantum state tomography. In prime and prime-power dimensions, analytical constructions of…
We prove a limit theorem for the the maximal interpoint distance (also called the diameter) for a sample of n i.i.d. points in the unit ball of dimension 2 or more. The exact form of the limit distribution and the required normalisation are…
We provide a general methodology for unbiased estimation for intractable stochastic models. We consider situations where the target distribution can be written as an appropriate limit of distributions, and where conventional approaches…
The notion of unbiased orthogonal designs is introduced as a generalization among unbiased Hadamard matrices, unbiased weighing matrices and quasi-unbiased weighing matrices. We provide upper bounds and several constructions for mutually…
Recently the problem of Unambiguous State Discrimination (USD) of mixed quantum states has attracted much attention. So far, bounds on the optimum success probability have been derived [1]. For two mixed states they are given in terms of…
For a nonempty compact set D of R we determine the maximal possible dimension of a subspace X of polynomial functions of degree at most m which possesses a positive bases (where positivity is understood on D). The exact value of this…
We have developed an algorithm that numericaly computes the dimension of an extremely inhomogeous matter distribution, given by a discrete hierarchical metric. With our results it is possible to analise how the dimension of the matter…
A complete set of N+1 mutually unbiased bases (MUBs) forms a convex polytope in the N^2-1 dimensional space of NxN Hermitian matrices of unit trace. As a geometrical object such a polytope exists for all values of N, while it is unknown…
We give tight lower and upper bounds on the expected missing mass for distributions over finite and countably infinite spaces. An essential characterization of the extremal distributions is given. We also provide an extension to totally…
We consider the inverse conductivity problem with discontinuous conductivities. We show in a rigorous way, by a convergence analysis, that one can construct a completely discrete minimization problem whose solution is a good approximation…
The distributionally robust Markov Decision Process (MDP) approach asks for a distributionally robust policy that achieves the maximal expected total reward under the most adversarial distribution of uncertain parameters. In this paper, we…