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**It is with enormous sadness that we have to report that Professor Paul Busch died on Saturday 9th June 2018 following a short illness. The Department will be collecting memories and thoughts of Paul for a book of condolences, and you are welcome to contribute to it by either using this page http://maths.york.ac.uk/paul-busch or by emailing maths-hod@york.ac.uk.**

For further information please visit Paul Busch’s personal Quantum Research Page.

I studied physics, mathematics and philosophy at the University of Cologne, where I obtained my first degree in Physics in 1979 and PhD in 1982. During my postdoctoral years at Cologne and Göttingen, I undertook investigations into a range of foundational problems of quantum theory and statistical physics. Following my habilitation, I was appointed University Docent in Theoretical in Cologne in 1988, and was awarded the title of Professor there in 1994. I held appointments as visiting professor and research scholar at a number of institutions including Florida Atlantic University (1986), the University of Heidelberg (in Philosophy, 1994), Harvard University (hosted by Roy Glauber, Lyman Laboratory of Physics, 1994/5), and the Perimeter Institute of Theoretical Physics (2005-2007). I also hold an adjunct professorship at the Department of Physics and Astronomy, University of Turku. I was professor of mathematical physics at the University of Hull and was Head of Department there from 2002 before joining the University of York in 2005. I am an editor of the “Foundations of Physics” journal and co-editor of the Springer monograph series "Fundamental Theories of Physics".

I was elected Member of L’Académie Internationale de Philosophie des Sciences in 2008, Fellow of the Institute of Physics in 2014, and Member of the Foundational Questions Institute (FQXi) in 2015. From 2016-2018, I am serving as President of the International Quantum Structures Association.

I have been awarded a Royal Society Leverhulme Trust Senior Research Fellowship (2017/18).

Chair of Graduate School Committee (2008-2012, 2015-2017)

Member, Departmental Research Committee (2008-2012, 2015-2017)

Head of Applied Mathematics Section (2008-2014)

Member, Science Advisory Group for Academic Staff Promotions (2007-2008)

My research interests lie in the interface between physics, mathematics and philosophy, centering around questions on the relationship between quantum and classical physics, relativistic quantum measurement and quantum information theory.

A focus in recent years has been the subject of *quantum uncertainty, *notably the theory of approximate joint measurements of incompatible observables and the study of associated measurement uncertainty relations, a subject of an ongoing scientific controversy. Much of my research is summarised in three (co-authored) monographs, “The Quantum Theory of Measurement” (Springer, 1991/1996), “Operational Quantum Physics” (Springer, 1995/1997), and "Quantum Measurement" (Springer, 2016).

For further information, please visit my *Quantum Research Page* and the associated *Quantum Uncertainty Page**, *which contains links to recent theoretical and experimental work on measurement uncertainty relations, including pedagogical material and associated Wolfram demonstrations.

My current main research interest is the development of the operational tools of quantum measurement theory (observables as POVMs, quantum operations), their application to the solution of conceptual problems and the modelling of practical measurement schemes. One strand of current work is concerned with structural aspects of finite-dimensional quantum systems (qudits), specifically the search for interesting measures of approximation and degrees of the unsharpness of quantum observables. Possible topics for PhD projects include the development of models of approximate joint measurements of families of incompatible observables, the exploration of measurement uncertainty relations and their implications for quantum metrology. Further possible directions include quantum measurement limitations due to symmetry and their consequences for quantum information processing. Another possible project area is that of relativistic quantum measurements (covariant collapse, localisation vs. causality). Finally, I’m interested in exploring measurement theoretic and dynamical aspects of the contrast between classical and quantum mechanics and the transition from quantum to classical for large systems.