Foundations of Physics, VoL 10, Nos. 9/10, 1980 On the Actual Measurability of the Density Matrix of a Decaying System by Means of Measurements on the Decay Products S. Bergia, 1 F. Cannata, 1 A. Cornia, 2 and R. LivP Received December 10, 1979 The density matrix p describing a decaying system can be expressed in terms of correlations among observables belonging to the subsystems. Due to this structure and to the difficulties in measuring higher rank tensors of decay products for a single decay event, it is found that the mean value of p cannot be determined, in general, from measurements on the decay products. We also discuss the consequences of this conclusion as far as tests of qttantum mechanics are concerned. 1. INTRODUCTION Let i ¢) be state vector of a composite system subject to a two-body decay. Spin, statistics, and conservation law symmetries imply that in general J ¢> is a state of the second kind? Concerning the statistical operator p = [ ¢)(¢r for this case, we first ask the following question: is it possible in general to express p in terms of actual observables belonging to the decay products ? It should be made clear from the beginning that it is impossible to determine the full (two-body) density matrix p from the mere knowledge of the density matrices pr and pX~ of the decay products. Indeed, p can be expressed as the direct product of p~ and pn if and only if I ¢) can in turn Istituto di Fisica dell'Universit~t, Bologna, Italy and Istituto Nazionale di Fisica Nucleare, Sezione di Bologna, Italy. 2 lstituto Nazionale di Fisica Nucleare, Sezione di Bologna, Italy and Scuola di Perfeziona- mento in Fisica, Universit~t di Bologna, Italy. Istituto Nazionale di Fisica Nucleare, Sezione di Trieste, Italy. 4 We recall that a state of the first kind is one that is a product of states of the constituent systems, and a state that is not a product is said to be of the second kind. 723 0015-9018180]1000-0723503.00/0 • 1980 Plenum Publishing Corporation