Exciting, Russ. I've downloaded your 2004 paper
<http://arxiv.org/pdf/physics/0001020v6>, and will take a look.
Thanks,
Grant
On 7/26/11 3:16 PM, Russell Standish wrote:
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/
*_____________________________________________*
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