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 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 …

We consider two related tasks:(a) estimating a parameterisation of a given Gibbs state and
expectation values of Lipschitz observables on this state;(b) learning the expectation values …

In the context of quantum theories of spacetime, one overarching question is how quantum
information in the bulk spacetime is encoded holographically in boundary degrees of …

Bayes' rule, P (B| A) P (A)= P (A| B) P (B), is one of the simplest yet most profound,
ubiquitous, and far-reaching results of classical probability theory, with applications in any …

The rates of quantum cryptographic protocols are usually expressed in terms of a conditional
entropy minimized over a certain set of quantum states. In particular, in the device …

We prove that the quantum relative entropy decreases monotonically under the application
of any positive trace-preserving linear map, for underlying separable Hilbert spaces. This …

This book is a love poem to Loewner's theorem. There are other mathematical love poems,
although not many. One sign, not always present and not foolproof, is that like this book, the …

Given a uniform, frustration-free family of local Lindbladians defined on a quantum lattice
spin system in any spatial dimension, we prove a strong exponential convergence in relative …

We formally extend the notion of Markov order to open quantum processes by accounting for
the instruments used to probe the system of interest at different times. Our description …