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Even though mutually unbiased bases and entropic uncertainty relations play an important role in quantum cryptographic protocols they remain ill understood. Here, we construct special sets of up to 2n+1 mutually unbiased bases (MUBs) in…
We have obtained the optimal upper bound of entropic uncertainty relation for $N$ Mutually Unbiased Bases (MUBs). We have used the methods of variational calculus for the states that can be written in terms of $N$ MUBs. Our result is valid…
Mutually unbiased bases correspond to highly useful pairs of measurements in quantum information theory. In the smallest composite dimension, six, it is known that between three and seven mutually unbiased bases exist, with a decades-old…
Determining the strength of non-linear statistical dependencies between two variables is a crucial matter in many research fields. The established measure for quantifying such relations is the mutual information. However, estimating mutual…
Mutually Unbiased Bases (MUBs) are closely connected with quantum physics, and the structure has a rich mathematical background. We provide equivalent criteria for extending a set of MUBs for $C^n$ by studying real points of a certain…
We begin by defining mutually unbiased (MU) observables on a finite dimensional Hilbert space. We also consider the more general concept of parts of MU observables. The relationships between MU observables, value-complementary observables…
A collection of orthonormal bases for a complex dXd Hilbert space is called mutually unbiased (MUB) if for any two vectors v and w from different bases the square of the inner product equals 1/d: |<v,w>| ^{2}=1/d. The MUB problem is to…
We show that in a complex d-dimensional vector space, one can find O(d) bases whose elements form a 2-design. Such vector sets generalize the notion of a maximal collection of mutually unbiased bases (MUBs). MUBs have manifold applications…
We study a quantum process reconstruction based on the use of mutually unbiased projectors (MUB-projectors) as input states for a D-dimensional quantum system, with D being a power of a prime number. This approach connects the results of…
Modern recommendation systems rank candidates by aggregating multiple behavioral signals through a value model. However, many commonly used signals are inherently affected by heterogeneous biases. For example, watch time naturally favors…
In the device-independent quantum information approach, the implementation of a given task can be self-tested solely from the recorded statistics and without detailed models for the employed devices. Even though experimentally demanding, it…
We present a systematic method to introduce free parameters in sets of mutually unbiased bases. In particular, we demonstrate that any set of m real mutually unbiased bases in dimension N>2 admits the introduction of (m-1)N/2 free…
We describe sets of mutually unbiased bases (MUBs) for quantum states defined over the p-adic numbers Q_p, i.e. the states that can be described as elements of the (rigged) Hilbert space L2(Q_p). We find that for every prime p>2 there are…
We discuss quantitatively the complementarity of information transmitted by a quantum system prepared in a basis state in one out of several different mutually unbiased bases (MUBs). We obtain upper bounds on the information available to a…
I consider the tradeoff between the information gained about an initially unknown quantum state, and the disturbance caused to that state by the measurement process. I show that for any distribution of initial states, the…
This paper introduces a general framework for estimating variance components in the linear mixed models via general unbiased estimating equations, which include some well-used estimators such as the restricted maximum likelihood estimator.…
We apply random matrix theory to study the impact of measurement uncertainty on dynamic mode decomposition. Specifically, when the measurements follow a normal probability density function, we show how the moments of that density propagate…
Prior works have explored multi-armed bandit (MAB) algorithms for the selection of optimal beams for millimeter-wave (mmW) communications between base station and mobile users. However, when the number of beams is large, the existing MAB…
This short note highlights the most prominent mathematical problems and physical questions associated with the existence of the maximum sets of mutually unbiased bases (MUBs) in the Hilbert space of a given dimension
We study mutually unbiased maximally entangled bases (MUMEB's) in bipartite system $\mathbb{C}^d\otimes\mathbb{C}^d (d \geq 3)$. We generalize the method to construct MUMEB's given in [16], by using any commutative ring $R$ with $d$…