This book concerns the foundations of Quantum Gravity, in particular from a conceptual point
of view. It provides a self-contained introduction to this topic, resting on particular features of …

We present a systematic geometric framework to study closed quantum systems based on
suitably chosen variational families. For the purpose of (A) real time evolution,(B) excitation …

This volume, setting out the theory of positive maps as it stands today, reflects the rapid
growth in this area of mathematics since it was recognized in the 1990s that these …

We show that the nonequilibrium entropy production for a driven quantum system is larger
than the Bures length, the geometric distance between its actual state and the …

Geometric phases are ubiquitous in physics; they act as memories of the transformation of a
physical system. In optics, the most prominent examples are the Pancharatnam-Berry phase …

A bstract In this work, we propose a testing procedure to distinguish between the different
approaches for computing complexity. Our test does not require a direct comparison …

The resource theory of quantum coherence studies the off-diagonal elements of a density
matrix in a distinguished basis, whereas the resource theory of purity studies all deviations …

We demonstrate that the Rényi-2 entropy provides a natural measure of information for any
multimode Gaussian state of quantum harmonic systems, operationally linked to the phase …

We calculate the quantum Cramér-Rao bound for the sensitivity with which one or several
parameters, encoded in a general single-mode Gaussian state, can be estimated. This …

Conventional quantum speed limits perform poorly for mixed quantum states: They are
generally not tight and often significantly underestimate the fastest possible evolution speed …