1) Quantum measurements and the third law of thermodynamics.
Noise can be considered the natural enemy of quantum information. An often implied benefit
of high-dimensional entanglement is its increased resilience to noise. However, manifesting this
potential in an experimental setting is challengingm, as the dimension is not really a free parameter and
different dimensions often imply different implementations. For discretising continuous degrees of
freedom, however, one can tune the Hilbert space dimension through discretisation and we show
how to explot two pathways to noise resilience in that context and demonstrate that high-dimensional
entanglement can indeed survive environmental conditions that no qubit encoding could survive.
2) Entanglement distribution beyond qubits.
The third law of thermodynamics can be phrased as an impossibility of cooling any physical system to
absolute zero temperature. The projection postulate of quantum mechanics, however, predicts pure
post-measurement states in idealised settings. We show how a self-contained treatment connects the
two concepts and extends the impossibility of cooling to the impossibility of perfect measurements or
Landauer erasure with finite thermodynamic resources. We will also discuss more quantitative trade-offs
between energy, time and complexity.