Quantum Foundations

In this talk I will report on a recent work [arXiv:0908.1583], which investigates general probabilistic theories where every mixed state has a purification, unique up to reversible channels on the purifying system. The purification principle is equivalent to the existence of a reversible realization for every physical process, namely that to the fact that every physical process can be regarded as arising from the reversible interaction of the input system with an environment that is eventually discarded.

For a quantum system with a d-dimensional Hilbert space, a symmetric informationally complete measurement (SIC) can be thought of as a set of d^2 pure states all having the same overlap. Constructions of SICs for composite systems usually do not make use of the composite structure but treat the system as a whole. Indeed for some cases, one can prove that a SIC cannot have the symmetry that one naturally associates with the composite structure.

A closer look at some proposed Gedanken-experiments on BECs promises to shed light on several aspects of reduction and emergence in physics. These include the relations between classical descriptions and different quantum treatments of macroscopic systems, and the emergence of new properties and even new objects as a result of spontaneous symmetry breaking.

Instrumentalism about the quantum state is the view that this mathematical object does not serve to represent a component of (non-directly observable) reality, but is rather a device solely for making predictions about the results of experiments. One honest way to be such an instrumentalist is a) to take an ensemble view (= frequentism about quantum probabilities), whereby the state represents predictions for measurement results on ensembles of systems, but not individual systems and b) to assign some specific level for the quantum/classical cut.