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/ > *_____________________________________________* > >
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