Quantum resource theories (QRTs) offer a highly versatile and powerful framework for
studying different phenomena in quantum physics. From quantum entanglement to quantum …

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

This largely self-contained book on the theory of quantum information focuses on precise
mathematical formulations and proofs of fundamental facts that form the foundation of the …

We derive quantum theory from purely informational principles. Five elementary axioms—
causality, perfect distinguishability, ideal compression, local distinguishability, and pure …

We show that quantum theory allows for transformations of black boxes that cannot be
realized by inserting the input black boxes within a circuit in a predefined causal order. The …

The field of classical stochastic processes forms a major branch of mathematics. Stochastic
processes are, of course, also very well studied in biology, chemistry, ecology, geology …

Currently, there is no systematic way to describe a quantum process with memory solely in
terms of experimentally accessible quantities. However, recent technological advances …

We present a framework to treat quantum networks and all possible transformations thereof,
including as special cases all possible manipulations of quantum states, measurements …

We investigate general probabilistic theories in which every mixed state has a purification,
unique up to reversible channels on the purifying system. We show that the purification …

Shor's factoring algorithm provides a superpolynomial speedup over all known classical
factoring algorithms. Here, we address the question of which quantum properties fuel this …