Related papers: The problem of mutually unbiased bases in dimensio…
We develop a new technique to construct mutually unbiased tripartite absolutely maximally entangled bases. We first explore the tripartite absolutely maximally entangled bases and mutually unbiased bases in $\mathbb{C}^{d} \otimes…
We prove tight entropic uncertainty relations for a large number of mutually unbiased measurements. In particular, we show that a bound derived from the result by Maassen and Uffink for 2 such measurements can in fact be tight for up to…
We report on a search for mutually unbiased bases (MUBs) in 6 dimensions. We find only triplets of MUBs, and thus do not come close to the theoretical upper bound 7. However, we point out that the natural habitat for sets of MUBs is the set…
In quantum mechanics, mutually unbiased bases (MUBs) represent orthonormal bases that are as "far apart" as possible, and their classification reveals rich underlying geometric structure. Given a complex inner product space, we construct…
Mutually unbiased bases (MUBs) play a key role in many protocols in quantum science, such as quantum key distribution. However, defining MUBs for arbitrary high-dimensional systems is theoretically difficult, and measurements in such bases…
Recent neural network and language models rely on softmax distributions with an extremely large number of categories. Since calculating the softmax normalizing constant in this context is prohibitively expensive, there is a growing…
Quantum systems with variables in ${\mathbb Z}(d)$ are considered. The properties of lines in the ${\mathbb Z}(d)\times {\mathbb Z}(d)$ phase space of these systems, are studied. Weak mutually unbiased bases in these systems are defined as…
We propose a new method of finding the mutually unbiased bases for three qubits. The key element is the construction of the table of striation-generating curves in the discrete phase space. We derive a system of equations in the Galois…
Mutually Unbiased bases has various application in quantum information procession and coding theory. There can be maximum d + 1 MUBs in C^d and d/2 +1 MUBs in R^d. But , over R^d MUBs are known to be non existent when d is odd and for most…
It is conjectured that the question of the existence of projective planes whose order is not a power of prime is intimately linked with the problem whether there exists a set of d+1 mutually unbiased bases in a d-dimensional Hilbert space…
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 study entanglement witness and present a construction of entanglement witnesses in terms of the mutually unbiased measurements (MUMs). These witnesses include the entanglement witnesses constructed from mutually unbiased bases (MUBs) as…
Mutually unbiased bases which is also maximally entangled bases is called mutually unbiased maximally entangled bases (MUMEBs). We study the construction of MUMEBs in bipartite system. In detail, we construct 2(p^a-1) MUMEBs in C^d\otimes…
Inspired by the many applications of mutually unbiased Hadamard matrices, we study mutually unbiased weighing matrices. These matrices are studied for small orders and weights in both the real and complex setting. Our results make use of…
Quantum measurements based on mutually unbiased bases are commonly used in quantum information processing, as they are generally viewed as being maximally incompatible and complementary. Here we quantify precisely the degree of…
In this paper, we prove that the existence of a complete set of mutually unbiased bases (MUBs) in N-dimensional Hilbert space implies the existence of a complete set of mutually orthogonal Latin squares (MOLSs) of order N. In particular, we…
This paper suggests a framework for the learning of discretizations of expensive forward models in Bayesian inverse problems. The main idea is to incorporate the parameters governing the discretization as part of the unknown to be estimated…
We have developed a general method for constructing a set of non-orthogonal bases with equal separations between all different basis' states in prime dimensions.It results that the corresponding bi-orthogonal counterparts are pairwise…
We derive new inequalities for the probabilities of projective measurements in mutually unbiased bases of a qudit system. These inequalities lead to wider ranges of validity and tighter bounds on entropic uncertainty inequalities previously…
We present a detailed computational and algebraic study of Mutually Unbiased Bases (MUBs) in finite-dimensional Hilbert spaces, with a particular focus on dimensions 2, 3, 4, and the challenging case of 6. Starting from the Hadamard-phase…