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

Quantum measurements play a fundamental role in quantum mechanics. Especially,
generalized quantum measurements provide a powerful and versatile tool to extract …

Measurements with randomly chosen settings determine many important properties of
quantum states without the need for a shared reference frame or calibration. They naturally …

Complex forms of quantum entanglement can arise in two qualitatively different ways: either
between many qubits or between two particles with higher-than-qubit dimension. While both …

We introduce two families of criteria for detecting and quantifying the entanglement of a
bipartite quantum state of arbitrary local dimension. The first is based on measurements in …

The Schmidt number represents the genuine entanglement dimension of a bipartite
quantum state. We derive simple criteria for the Schmidt number of a density matrix in …

The most common form of measurement in quantum mechanics projects a wavefunction
onto orthogonal states that correspond to definite outcomes. However, generalized quantum …

Violation of Bell's inequalities shows strong conflict between quantum mechanics and local
realism. Loophole-free Bell tests not only deepen understanding of quantum mechanics, but …

Photons offer the potential to carry large amounts of information in their spectral, spatial, and
polarisation degrees of freedom. While state-of-the-art classical communication systems …

In the minimal scenario of quantum correlations, two parties can choose from two
observables with two possible outcomes each. Probabilities are specified by four marginals …