Probability tables

Suppose that we have written, in a sort of table, the statistical data collected from a group of experiments — the nature of which can be classical, quantum, or something else. Suppose that we also want to store this table’s data in a compact way. How could we proceed? In this paper it is shown that, given the situation described above, when we try to store or organise the table’s data in a more compact way we find that real vectors can be associated to preparations and results, in a way which, for quantum mechanical phenomena, is essentially the same as Hardy’s representation of ‘states’ and ‘measurement outcomes’ [1]. This curious fact may offer new points of view for looking at some of the current ‘foundational’ issues in quantum mechanics. The ideas here presented are a summary of those developed in Ref. 2, to which the Reader is referred for further details. The emphasis in this paper is on the main idea of a ‘table decomposition’, and on the implications of the latter for various topics discussed in this Conference.