Recent years have seen significant advances in the study of symmetric informationally
complete (SIC) quantum measurements, also known as maximal sets of complex …

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 …

It is often of interest to identify a given number of points in projective space such that the
minimum distance between any two points is as large as possible. Such configurations yield …

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 …

We give an overview of some remarkable connections between symmetric informationally
complete measurements (SIC-POVMs, or SICs) and algebraic number theory, in particular, a …

A family of separability criteria based on correlation matrix (tensor) is provided. Interestingly,
it unifies several criteria known before like, eg, computable cross-norm or realignment …

We present a conjectured family of symmetric informationally complete positive operator
valued measures which have an additional symmetry group whose size is growing with the …

The existence of pairwise equiangular complex lines [equivalently, a symmetric
informationally complete positive operator-valued measure (SIC-POVM)] in-dimensional …

Overlap between quantum states or observables is a fundamental quantity in quantum
theory. Equioverlapping measurements arise naturally when considering quantum …

We describe a general procedure for associating a minimal informationally complete
quantum measurement with a purely probabilistic representation of the Born rule. Such …