[FRIAM] Deriving quantum theory from information processing axioms

Grant Holland grant.holland.sf at gmail.com
Tue Jul 26 14:33:15 EDT 2011


I had the same feeling about my recent missive - entitled "Uncertainty 
vs Information - redux and resolution" - in which I too make various 
claims about information theory. I believe I had only one response - 
from Eric. I expected more, maybe from Owen and Frank and yourself.

The APS Physics review you attached discussed an Italian paper from the 
U of Pavia. About that paper the review says "They show that by making 
six fundamental assumptions about how information is processed, they can 
derive quantum theory."  Understandably, such a view is likely to be 
sacrosanct among many.

I must confess however that I have considerable sympathy with it. In my 
recent posting on /Uncertainty and Information/, I cited the Oxford Info 
Theorist Vlatko Vedral.  In his book _Decoding Reality: The Universe as 
Quantum Information_, he states:

"This book will state that information (and not matter or energy or 
love) is the building block on which everything is constructed. 
Information is far more fundamental than matter or energy because it can 
be successfully applied to both macroscopic interactions, such as 
economic and social phenomena, and, as I will argue, information can 
also be used to explain the origin and behavior of microscopic 
interactions such as energy and matter."

Evidently, there is a body of information theorist out there who are 
making a play for the proposition that  Information Theory is more 
fundamental than physics.

Of course, my recent posting argues that uncertainty is more 
foundational then information (even though, according to Shannon, 
entropy measures them both). This is because, as argued by Khinchin, 
information derives from uncertainty through realization.

Maybe together we can get a thread started about the primacy of physics, 
information or uncertainty - or maybe something else? Oh, yeah, there is 
already one going about the primacy of physics vs philosophy. Maybe we 
can add information and uncertainty to the mix!

On 7/26/11 11:37 AM, 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 <russ.abbott at gmail.com 
> <mailto: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 ?_A  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 ?_AB .
>         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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