With the rapid development of quantum technologies, a pressing need has emerged for a
wide array of tools for the certification and characterization of quantum devices. Such tools …

A thoroughly revised and updated edition of this introduction to modern statistical methods
for shape analysis Shape analysis is an important tool in the many disciplines where objects …

Intuitively, if a density operator has small rank, then it should be easier to estimate from
experimental data, since in this case only a few eigenvectors need to be learned. We prove …

Well-controlled quantum devices with their increasing system size face a new roadblock
hindering further development of quantum technologies. The effort of quantum tomography …

In recent years, Bayesian methods have been proposed as a solution to a wide range of
issues in quantum state and process tomography. State-of-the-art Bayesian tomography …

Quantum tomography has come a long way from early reconstructions of Wigner functions
from projections along quadratures to the full characterization of multipartite systems. Now, it …

Feasible tomography schemes for large particle numbers must possess, besides an
appropriate data acquisition protocol, an efficient way to reconstruct the density operator …

Quantum state tomography suffers from the measurement effort increasing exponentially
with the number of qubits. Here, we demonstrate permutationally invariant tomography for …

In the light of the progress in quantum technologies, the task of verifying the correct
functioning of processes and obtaining accurate tomographic information about quantum …

Quantum state tomography on a d-dimensional system demands resources that grow rapidly
with d. They may be reduced by using model selection to tailor the number of parameters in …