Regensburg 2022 – scientific programme

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QI: Fachverband Quanteninformation

QI 14: Quantum Foundations

QI 14.8: Talk

Friday, September 9, 2022, 11:45–12:00, H9

Geometry of expectation values of non-commuting observables — •Konrad Szymanski — Universität Siegen, Siegen, Deutschland

Non-commutativity lies at the heart of quantum theory and provides a rich set of mathematical and physical questions. Here, I address this topic through the concept of the Joint Numerical Range (JNR) – the set of simultaneously attainable expectation values for multiple quantum observables, which in general need not commute. I discuss mathematical and physical implications of the geometry of JNR: classification of the possible shapes of the set, as well as development of novel uncertainty relations, entanglement and Schmidt rank witnesses, and detection of vanishing energy gap.