The rapid developments in techniques of quantum experiments have given
rise to quite new subjects in theoretical quantum physics such as, for
example, quantum information, quantum cryptography, etc. The
developments in these theoretical fields play a fundamental role for
the design of new experiments, important for applications.
From the other side, all new theoretical topics on quantum measurements are essentially based on the elements of quantum measurement theory and, hence, any fundamental developments of quantum measurement theory have an immediate feedback to quantum physics. However, since quantum measurement theory is based, in general, on complex mathematical structures, its further development and understanding is not possible without the profound interplay with stochastic analysis. "Quantum stochastics" is just a new and intensively developing mathematical discipline representing this interplay.
The main aim of the International Joint MaPhySto and QUANTOP Workshop on Quantum Measurements and Quantum Stochastics was to get together the leading physicists and mathematicians, working in the above-mentioned fields, for intensive exchange of ideas and important results.
At the beginning of August 2003 I attended the inaugural Frontiers of Science symposium of the Australian Academy of Science in Canberra. To their credit, the organizers asked the attendees to evaluate its success in encouraging cross-disciplinary science. I learnt much at the meeting, but had to say that "To really encourage multidisciplinary research I think would require much more focussed meetings involving a few disciplines that would be likely to be able to forge links in a particular area."
I wrote these words (non-self-consciously) on the train from Copenhagen airport to Århus, to attend exactly such a focussed meeting: the 2003 Quantum Measurement and Quantum Stochastics workshop, hosted jointly by MaPhySto and QUANTOP. On the basis of my previous attendance at the 1999 workshop on Stochastics and Quantum Physics, I had high expectations for this one. I am pleased to say that the 2003 workshop exceeded my expectations in both the quality of presentations and the degree of interaction between researchers from different fields. In this report I will present merely a few personal highlights.
A striking development in the past 4 years has been the advance in experiments to the point where many of the sophisticated ideas in quantum state and parameter estimation of the last 30 years can now be implemented. We heard from C. Wunderlich about state estimation of two-level systems: of the joint ("entangled") measurement of a string of ions, and of his own work in the adaptive measurements of a succession of identically prepared ions. Then we heard from H. Mabuchi of phase estimation using real-time adaptive homodyne measurements on a single optical mode. An important message from Mabuchi's talk was the usefulness of feedback in providing the most robust measurement even in situations where a non-adaptive technique would be better in theory, and the existence of a large body of mathematics ("control theory") addressing such usefulness.
The field of theoretical quantum state and parameter estimation was represented by several speakers, including one of its founders, A. Holevo. There was a lively discussion after talks about the relationships between, and merits of, state estimation using maximum likelihood, maximum entropy, and inverse methods.
However, there is no doubt that the liveliest discussion at the workshop concerned the interpretation of measurements in quantum mechanics. This was central to the talks by E. Loubenets, V. Belavkin, A. Peres, and C. Fuchs, and was touched upon in my talk. It dominated the Discussion Session on Monday afternoon, where views on the significance and plausibility of radical Bayesianism, super-selection rules, ontic quantum states, Bohmian mechanics, and decoherence were exchanged vigorously and productively. At this session we also heard many words of wisdom from the chair, R. Gill, including an admonition that one should generalize problems, not solutions.
Still on this topic (which also dominated many meal-time conversations), I have to say that for me, and a number of others, the highlight of the workshop was the short presentation by the young philosopher/physicist R. Spekkens. He presented a model of "toy-bits"which really shed light upon the differences between classical and quantum information theory. In particular it revealed which features of the latter are due merely to limitations upon the knowledge one can obtain about a system, and which (such as contextuality and non-locality) point towards something deeper.
There were many other presentations that were of great interest to me and the other attendees, but there is no space to continue. As I write these words, on the train from Århus to Copenhagen airport, I am already missing the heady atmosphere of Århus, where, dining by the waterside on Åboulevarden, one could without warning find oneself engaged with an eminent physicist in a discussion about Bohm's treatment of quantum measurements.