There is another issue which one must also consider when attempting to
specify "fundamentality"; it must be taken in context. For example, there
are different meanings of 'fundamental' - one being constituitive, while
another is 'relationship' based (one before the other .... if you know what
I mean). Finally, there is the fundamentality of what 'things' *are* - which
is basically unanswerable.
For example, what *is* matter, what *is* energy, and what *is*
information? I don't think any of these can be decomposed into anything
else more 'fundamental' - they simply are. However, the fundametal
*particles* of matter may be electrons, quarks etc. Information does not,
instrinsically, have a 'fundamental' unit, though one has been defined as
the 'bit', while for energy the same can be said (I think ....), but with
various units defined and accepted.
Felix made a good observation RE: the qualitative vs the quantitative
natures of information. I can't say too much about this, except that I think
'meaning' or perhaps another word is more appropriate when speaking
about the qualitative aspects of information.
As an aside, Einstein has already shown the equivalence between
energy and matter, while Michael Nielsen's comment regarding error
correction for reversible architectures (he describes error correction as
a procedure for lowering the entropy of a physical system, which
consequently results in heat ie. energy being dissipated into the
environment) is an example that shows there are strong connections
between 'energy' and 'information'. (Another exampe, the entropy of a
physical system is calculated in terms of energy in joules or calories,
while the entropy in information theory is in terms of bits).