Of course, I published a paper in 2004 (Why Occams Razor) doing essentially the same thing (I expanded on this somewhat in my 2006 book, Theory of Nothing).
I would also say, that Lucien Hardy did something similar in 2001 (Quantum theory from five reasonable axioms). Also, there have been other works linking the uncertainty principle to the Cramer-Rao inequality from information theory. I expect this current paper (when I finally get around to read it), will be equivalent to what I've done. Ultimately, it may come down to history which method is preferred, or if some uber-clear version is presented (like Dirac did to Schroedinger and Heisenberg's theories). It would be all the more remarkable if this approach was fundamentally different. All I have to say now... On Tue, Jul 26, 2011 at 10:37:46AM -0700, Russ Abbott wrote: > I expected this to have more of an impact than it seems to be having. What > am I missing? > > *-- Russ Abbott* > *_____________________________________________* > *** Professor, Computer Science* > * California State University, Los Angeles* > > * Google voice: 747-*999-5105 > * blog: *http://russabbott.blogspot.com/ > vita: http://sites.google.com/site/russabbott/ > *_____________________________________________* > > > > On Mon, Jul 25, 2011 at 2:50 PM, Russ Abbott <[email protected]> wrote: > > > From APS Physics <http://physics.aps.org/articles/v4/55>. > > > > We know how to use the “rules” of quantum physics to build lasers, > > microchips, and nuclear power plants, but when students question the rules > > themselves, the best answer we can give is often, “The world just happens to > > be that way.” Yet why are individual outcomes in quantum measurements > > random? What is the origin of the Schrödinger equation? In a paper > > [1<http://physics.aps.org/articles/v4/55#c1>] > > appearing in Physical Review A, Giulio Chiribella at the Perimeter > > Institute inWaterloo, Canada, and Giacomo Mauro D’Ariano and Paolo > > Perinotti at the University of Pavia, Italy, offer a framework in which to > > answer these penetrating questions. They show that by making six fundamental > > assumptions about how information is processed, they can derive quantum > > theory. (Strictly speaking, their derivation only applies to systems that > > can be constructed from a finite number of quantum states, such as spin.) In > > this sense, Chiribella et al.’s work is in the spirit of John Wheeler’s > > belief that one obtains “it from bit,” in other words, that our account of > > the universe is constructed from bits of information, and the rules on how > > that information can be obtained determine the “meaning” of what we call > > particles and fields. > > ... > > > > They assume five new elementary axioms—causality, perfect > > distinguishability, ideal compression, local distinguishability, and pure > > conditioning—which define a broad class of theories of information > > processing. For example, the causality axiom—stating that one cannot signal > > from future measurements to past preparations—is so basic that it is usually > > assumed a priori. Both classical and quantum theory fulfil the five > > axioms. What is significant about Chiribella et al.’s work is that they > > show that a sixth axiom—the assumption that every state has what they call a > > “purification”—is what singles out quantum theory within the class. In fact, > > this last axiom is so important that they call it a postulate. The > > purification postulate can be defined formally (see below), but to > > understand its meaning in simple words, we can look to Schrödinger, who in > > describing entanglement gives the essence of the postulate: “Maximal > > knowledge of a total system does not necessarily include maximal knowledge > > of all its parts.” (Formally, the purification postulate states that every > > mixed state ρA of system A can always be seen as a state belonging to a > > part of a composite system AB that itself is in a pure state ΨAB. This > > pure state is called “purification” and is assumed to be unique up to a > > reversible transformation on B). > > > > Chiribella et al. conclude there is only one way in which a theory can > > satisfy the purification postulate: it must contain entangled states. (The > > other option, that the theory must not contain mixed states, that is, that > > the probabilities of outcomes in any measurement are either 0 or 1 like in > > classical deterministic theory, cannot hold, as one can always prepare mixed > > states by mixing deterministic ones.) The purification postulate alone > > allows some of the key features of quantum information processing to be > > derived, such as the no-cloning theorem or teleportation > > [7<http://physics.aps.org/articles/v4/55#c7>]. > > By combining this postulate with the other five axioms, Chiribella et al. > > were > > able to derive the entire mathematical formalism behind quantum theory. > > > > > > > > *-- Russ Abbott* > > *_____________________________________________* > > *** Professor, Computer Science* > > * California State University, Los Angeles* > > > > * Google voice: 747-*999-5105 > > * blog: *http://russabbott.blogspot.com/ > > vita: http://sites.google.com/site/russabbott/ > > *_____________________________________________* > > > > > ============================================================ > FRIAM Applied Complexity Group listserv > Meets Fridays 9a-11:30 at cafe at St. John's College > lectures, archives, unsubscribe, maps at http://www.friam.org -- ---------------------------------------------------------------------------- Prof Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders Visiting Professor of Mathematics [email protected] University of New South Wales http://www.hpcoders.com.au ---------------------------------------------------------------------------- ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org
