Random numbers are a fundamental resource in science and engineering with important
applications in simulation and cryptography. The inherent randomness at the core of …

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

E-commerce, a type of trading that occurs at a high frequency on the internet, requires
guaranteeing the integrity, authentication, and nonrepudiation of messages through long …

We review selected advances in the theoretical understanding of complex quantum many-
body systems with regard to emergent notions of quantum statistical mechanics. We cover …

Heisenberg's uncertainty principle forms a fundamental element of quantum mechanics.
Uncertainty relations in terms of entropies were initially proposed to deal with conceptual …

Finally, here is a modern, self-contained text on quantum information theory suitable for
graduate-level courses. Develo** the subject'from the ground up'it covers classical results …

Quantum classification and hypothesis testing (state and channel discrimination) are two
tightly related subjects, the main difference being that the former is data driven: how to …

The early Gottesman, Kitaev, and Preskill (GKP) proposal for encoding a qubit in an
oscillator has recently been followed by cat-and binomial-code proposals. Numerically …

The security of conventional cryptography systems is threatened in the forthcoming era of
quantum computers. Quantum key distribution (QKD) features fundamentally proven security …

Bell's 1964 theorem, which states that the predictions of quantum theory cannot be
accounted for by any local theory, represents one of the most profound developments in the …