Semidefinite programs are convex optimization problems involving a linear objective
function and a domain of positive-semidefinite matrices. Over the past two decades, they …

'The book is very well-written by one of the leading figures in the subject. It is self-contained,
includes relevant recent advances and is enriched by a large number of examples and …

Graphs are usually represented as geometric objects drawn in the plane, consisting of
nodes and curves connecting them. The main message of this book is that such a …

We develop further the new versions of quantum chromatic numbers of graphs introduced by
the first and fourth authors. We prove that the problem of computation of the commuting …

This paper presents a comprehensive exploration of semi-definite programming (SDP)
techniques within the context of quantum information. It examines the mathematical …

We introduce a notion of quantum function and develop a compositional framework for finite
quantum set theory based on a 2-category of quantum sets and quantum functions. We use …

We derive one-shot upper bounds for quantum noisy channel codes. We do so by regarding
a channel code as a bipartite operation with an encoder belonging to the sender and a …

We investigate the classical communication over quantum channels when assisted by no-
signaling and positive-partial-transpose-preserving (PPT) codes, for which both the optimal …

We define several new types of quantum chromatic numbers of a graph and characterize
them in terms of operator system tensor products. We establish inequalities between these …

Unextendible product bases (UPBs) play a key role in the study of quantum entanglement
and nonlocality. Here we provide an equivalent characterization of UPBs in graph-theoretic …