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

Starting from a state of low quantum entanglement, local unitary time evolution increases the
entanglement of a quantum many-body system. In contrast, local projective measurements …

We review various bounds concerning out-of-equilibrium dynamics in few-level and many-
body quantum systems. We primarily focus on closed quantum systems but will also mention …

We consider quantum many-body dynamics under quantum measurements, where the
measurement-induced phase transitions (MIPs) occur when changing the frequency of the …

This is a preliminary version of a book in progress on the theory of quantum communication.
We adopt an information-theoretic perspective throughout and give a comprehensive …

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 …

Quantum resource theories have been widely studied to systematically characterize the
nonclassicality of quantum systems. Most resource theories focus on quantum states and …

The quantum Fourier transform (QFT) is a key component of many important quantum
algorithms, most famously being the essential ingredient in Shor's algorithm for factoring …

To achieve universal quantum computation via general fault-tolerant schemes, stabilizer
operations must be supplemented with other non-stabilizer quantum resources. Motivated …

Quantum channels underlie the dynamics of quantum systems, but in many practical settings
it is the channels themselves that require processing. We establish universal limitations on …