From: scerir (scerir@libero.it)
Date: Thu Mar 28 2002 - 00:54:30 MST
> I agree that it is paradoxical that a system can have an infinite number
> of possible states, each distinct at least in theory, and yet it can hold
> only one bit of information. I don't have a good explanation of this,
> other than that maybe you could say that the number of bits per internal
> state is infinitisimal. I don't know if that really works, but it
> suggests another place where fractional bits come into play.
> Hal
'In principle' an infinite amount of information can be coded
in a spin 1/2 system (that is - but I'm not sure - proved
by quantum computation). That's because each point on the
'Poincarč sphere' (and they are infinite) is a quantum state,
for a spin 1/2 system. Thus a spin 1/2 quantum system has
an infinite number of 'possible' (which does not mean
'accessible') states.
But unfortunately, with this QM, a quantum state of the
spin is not an 'observable'. Thus we must stay with
the well known 'upper bound' for a spin 1/2 system,
which is typically quantum-mechanical, which is = 1 bit,
and which gives us the amount of the 'measurement-accessible-
information'.
[see B. W. Schumacher, Information for Quantum Measurements,
in 'Complexity, Entropy and the Physics of Information,
Addison-Wesley, 1990, ed. W. Zurek]
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