A universal property for sequential measurement

Abstract

We study the sequential product the operation p * q = √pq√p on the set of effects, [0,1]A, of a von Neumann algebra A that represents sequential measurement of first p and then q. In their work [J. Math. Phys. 49(5), 052106 (2008)], Gudder and Latrémolière give a list of axioms based on physical grounds that completely determines the sequential product on a von Neumann algebra of type I, that is, a von Neumann algebra B(H) of all bounded operators on some Hilbert space H. In this paper we give a list of axioms that completely determines the sequential product on all von Neumann algebras simultaneously (Theorem 4).