18 - Letters to David Mermin

Summary

September 1996, “Theorem II”

I encountered your “Ithaca Interpretation” paper this morning on the quant-ph archive … and, I must say, I've been walking around with a nice feeling since. There are some things in it that I like very much!

Your Theorem II (or a very slight variation of it) has indeed been proven before, by Bill Wootters. I'll attach the citations below along with part of a note Bill once sent me. (Interestingly, one can also make a cut between real, complex, and quaternionic Hilbert spaces based on such a theorem.)

About your Theorem I, if I am not mistaken, it also has a history that predates the references you gave. I believe Richard Jozsa once told me that a fellow named Hadjisavvas found it well before HJW and Gisin. If you are interested you can contact Richard directly; his e-mail address is.…

As I say, I enjoyed your paper very much! (Presently) I think my only point of departure in what you say is about the issue of “objective probability.” Carl Caves and I (in still another paper cited below which can be found on quant-ph, pp. 22–26 in particular) have advocated the view that even the probabilities of quantum theory should be interpreted in a Bayesian or subjective way. We prefer to say that it is the “indeterminism” of quantum mechanics that is “objective,” and not the probabilities themselves.