From: scerir (scerir@libero.it)
Date: Wed Mar 27 2002 - 14:28:32 MST
[Anton Zeilinger]
> > That is to say, information is quantized.
[Hal]
> Actually, information is not quantized.
Zeilinger was speaking about the 'physics'
of information, I suppose, and not about
information, or knowledge.
Anyway it is interesting to point out, here,
that there is an information-theoretic
approach to Bell's inequalities (Braunstein,
Caves, Schumacher, and somehow also Cerf and
Adami). These authors showed that, if Bell's
inequalities are violated by QM, there is an
information deficit, increasing with increasing
spin number.
It is of great interest the existence of bounds
for the information gain. Holevo, i.e., proved
the existence of an upper bound for the information
one can extract from a quantum system. In the
quantum case - this is the point - an infinite
amount of information transfer would require
an infinite entropy of the measured system.
Hence Holevo's theorem is a confirmation of the
impossibility to measure (by a single measurement,
but there are also Zeno-effect- measurements!)
the so called 'density matrix' of a system (which
represents the maximal amount of information
contained in a quantum system).
A spin 1/2 system has an information capacity =
1 bit. But a spin 1/2 system has an infinite
number os states (see the 'Poincarč sphere').
Hence an infinite amount of information could,
in principle, be coded in a spin 1/2 system!
The 't Hooft's holographic bound [1993]
S < A / 4 h-bar
where A is a surface around a physical system
and S is information (assuming G = c = 1)
is also a well known bound. As far as I remember
it means that 10^66 bits of information could
be stored in a 1 cm^3 cube [or not? hmmm].
Bekenstein's original bound. Well known is
also the Bekestein's bound [1981 ?].
Both these bounds share the 'h-bar'. Thus
'physical' information must have something
to do, at least, with this h-bar !
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