Licentiate Thesis: Configurations in Quantum Information

by Kate Blanchfield (Stockholm University, Department of Physics)

Monday 19 Nov 2012, 11:00 → 13:00 Europe/Stockholm

FB54 (AlbaNova)

Measurements play a central role in quantum information. This thesis looks at two types: contextual measurements and symmetric measurements. Contextuality originates from the Kochen-Specker theorem about hidden variable models and has recently undergone a subtle shift in its manifestation. Symmetric measurements are characterised by the regular polytopes they form in Bloch space (the vector space containing all density matrices) and are the subject of several investigations into their existence in all dimensions. We often describe measurements by the vectors in Hilbert space onto which our operators project. In this sense, both contextual and symmetric measurements are connected to special sets of vectors. These vectors are often special for another reason: they form configurations in a given incidence geometry. In this thesis, we aim to show various connections between configurations and measurements in quantum information. The configurations discussed here would have been well-known to 19th and 20th century geometers and we show they are relevant for advances in quantum theory today. Specifically, the Hesse and Reye configurations provide proofs of measurement contextuality, both in its original form and its newer guise. The Hesse configuration also ties together different types of symmetric measurements in dimension 3—called SICs and MUBs—while giving insights into the group theoretical properties of higher dimensional symmetric measurements.