Abstract

In this work, quantum theories are considered which consist in essence of a map from state preparation proceduresw to states and a map from decision proceduresQ to probability operator measures. Two definitions of validity, similar to that given elsewhere, are given and compared for these theories. One definition is given in terms of one carrying out of somew followed by someQ, denoted by(Q, w). The other is given in terms of infinite repetitions(Q, w) ofw followed byQ. Both definitions are discussed in terms of the comparison of limit empirical means with theoretical expectation values. Particular attention is given to the use of outcome sequences of(Q, w) and of(Q, w) to determine properties of the probability measures the physical theory assigns to each(Q, w) in its domain