Related papers: Mutually unbiased bases, orthogonal Latin squares,…
Quantum Latin squares are a generalization of classical Latin squares in quantum field and have wide applications in unitary error bases, mutually unbiased bases, $k$-uniform states and quantum error correcting codes. In this paper, we put…
We relate the construction of a complete set of cyclic mutually unbiased bases, i. e., mutually unbiased bases generated by a single unitary operator, in power-of-two dimensions to the problem of finding a symmetric matrix over F_2 with an…
Whenever a mathematical proposition to be proved requires more information than it is contained in an axiomatic system, it can neither be proved nor disproved, i.e. it is undecidable, or logically undetermined, within this axiomatic system.…
Mutually unbiased bases (MUB) are an elusive discrete structure in Hilbert spaces. Many (complete sets of) MUB are group covariant, but little is known whether they can be sharply covariant in the sense that the generating groups can have…
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…
Measuring incomplete sets of mutually unbiased bases constitutes a sensible approach to the tomography of high-dimensional quantum systems. The unbiased nature of these bases optimizes the uncertainty hypervolume. However, imposing…
Complementarity is a phenomenon explaining several core features of quantum theory, such as the well-known uncertainty principle. Roughly speaking, two objects are said to be complementary if being certain about one of them necessarily…
An efficient method for assessing the quality of quantum state tomography is developed. Special attention is paid to the tomography of multipartite systems in terms of unbiased measurements. Although the overall reconstruction errors of…
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…
A collection of pairwise mutually unbiased bases (in short: MUB) in d>1 dimensions may consist of at most d+1 bases. Such "complete" collections are known to exists in C^d when d is a power of a prime. However, in general little is known…
An essential feature of genuine quantum correlation is the simultaneous existence of correlation in complementary bases. We reveal this feature of quantum correlation by defining measures based on invariance under a basis change. For a…
Goyeneche et al.\ [Phys.\ Rev.\ A \textbf{97}, 062326 (2018)] introduced several classes of quantum combinatorial designs, namely quantum Latin squares, quantum Latin cubes, and the notion of orthogonality on them. They also showed that…
The paper reviews and discusses four ideas scattered in previous papers of the author. First, objective properties of quantum systems are not associated with observables but are defined by preparations. Second, measurable results of…
Mutually unbiased bases of a Hilbert space can be constructed by partitioning a unitary error basis. We consider this construction when the unitary error basis is a nice error basis. We show that the number of resulting mutually unbiased…
The hidden-variable question is whether or not various properties --- randomness or correlation, for example --- that are observed in the outcomes of an experiment can be explained via introduction of extra (hidden) variables which are…
Mutually unbiased bases that can be cyclically generated by a single unitary operator are of special interest, since they can be readily implemented in practice. We show that, for a system of qubits, finding such a generator can be cast as…
Akin to the idea of complete sets of Mutually Unbiased Bases for prime dimensional Hilbert spaces, $\mathcal{H}_d$, we study its analogue for a $d$ dimensional subspace of $M (d,\mathbb{C})$, i.e. Mutually Unbiased Unitary Bases (MUUBs)…
We present a new approach to the problem of mutually unbiased bases (MUBs), based on positive definite functions on the unitary group. The method provides a new proof of the fact that there are at most $d+1$ MUBs in ${\mathbb C}^d$. It may…
All mutually unbiased bases in dimension six consisting of product states only are constructed. Several continuous families of pairs and two triples of mutually unbiased product bases are found to exist but no quadruple. The exhaustive…
Entropic uncertainty relations provide an information-theoretic framework for quantifying the fundamental indeterminacy inherent in quantum mechanics. We propose more stringent quantum-memory-assisted entropic uncertainty relations for…