Linear optics underpins fundamental tests of quantum mechanics and quantum
technologies. We demonstrate a single reprogrammable optical circuit that is sufficient to …

Quantum information theory is a branch of science at the frontier of physics, mathematics,
and information science, and offers a variety of solutions that are impossible using classical …

This book gives a unified introduction to the rapidly developing area of finite tight frames.
Fifteen years ago, the existence of equal-norm tight frames of n> d vectors for Rd and Cd …

We identify five selected open problems in the theory of quantum information, which are
rather simple to formulate, are well studied in the literature, but are technically not easy. As …

Mutually unbiased bases (MUBs) constitute the canonical example of incompatible quantum
measurements. One standard application of MUBs is the task known as quantum random …

We identify five selected open problems in the theory of quantum information, which are
rather simple to formulate, were well-studied in the literature, but are technically not easy. As …

The intended purpose of this work is to provide the reader with a comprehensive, state-of-
the art presentation of the theory of complex Hadamard matrices, or at least report on the …

We present an infinite number of construction schemes involving unitary error bases,
Hadamard matrices, quantum Latin squares and controlled families, many of which have not …

In this paper we describe some new algebraic features of the Gram matrices of complex
Equiangular Tight Frames (ETF). This lead on the one hand to the nonexistence of several …

This paper is a survey of contemporary results and applications of the theory of homotopes.
The notion of a well-tempered element of an associative algebra is introduced, and it is …