Wei writes:
> I just found a paper which shows that if apparent quantum randomness has 
> low algorithmic complexity (as Schmidhuber II predicts), then FTL 
> communications is possible.
>
> http://arxiv.org/abs/quant-ph/9806059

This was an interesting paper but unfortunately the key point seemed
to pass by without proof.  On page 5, the proposal is to use entangled
particles to try to send a signal by measuring at one end in a sequence
of different bases which are chosen by an algorithmically incompressible
mechanism.  The assumption is that this will result in an algorithmically
incompressible set of results at both ends, in contrast to the state
where stable measurements are done, which we assume for the purpose of
the paper produces algorithmically compressible results.

The author writes: "This process of scrambling with the random template T
guarantees that Bob's modified N-bit long string of quantum measurements
is almost surely p-incompressible..., and that Alice's corresponding
string (which is now different from Bob's) is also (almost surely)
p-incompressible"

It's not clear to me that this follows.  Why couldn't Bob's measurement
results, when using a randomly chosen set of bases, still have a
compressible structure?  And why couldn't Alice's?

Also, does this result depend on the choice of an unbalanced system
with alpha and beta different from 1/2?  This short description of
the signalling process doesn't seem to refer explicitly to special
alpha/beta values.

If not, could the procedure be as simple as choosing to measure in
the X vs + bases, as is often done in quantum crypto protocols?  If we
choose between X and + using an algorithmically incompressible method,
will that guarantee that the measured values are also incompressible?

Hal Finney

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