[FRIAM] Deriving quantum theory from information processing axioms

Russ Abbott russ.abbott at gmail.com
Tue Jul 26 13:37:46 EDT 2011

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 <russ.abbott at gmail.com> 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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