Russ,
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.abb...@gmail.com
<mailto:russ.abb...@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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