🚀 go-pugleaf

In article <TK.92Oct12131052@entropy.ai.mit.edu>, tk@ai.mit.edu (Tom Knight)
writes:
| You would think that a single photon could be amplified, for example
| in a laser-like structure to produce additional copies.  Measuring one
| of the copies in one polarization, and another in the orthogonal
| polarization, would give the complete answer to the question of the
| state of the original particle, destroying the cryptanalytic basis of
| quantum cryptography.  Unfortunately (or fortunately if you are a
| cryptographer), there is intrinsic noise associated with the
| amplification process, in just the amount required to prevent this
| process from succeeding.  If you want to look at the details of the
| quantum mechanics, look at e.g. "Quantum noise in linear amplifiers"
| H.A. Haus and J.A. Muller, Phys. Rev. Vol 128 pp 2407-2413 (1962).  It
| is perhaps most easily accesible in the excellent collection "Quantum
| Theory and Measurement" edited by Wheeler and Zurek, Princeton U.
| Press, 1983.

Hold on a moment!  This and other comments have tried to do too much.
Remember, the original point was not to try to find a hole in QM, it was to
read the apparently secret messages that Alice sent Bob.  The basis of the
secrecy was that an eavesdropper could not measure the state of a photon
before passing it onto Bob without Alice and Bob knowing about it.  But
in fact the assumption needed was stronger:  That the eavesdropper couldn't
even *duplicate* the photon's state without Alice and Bob knowing.  THAT
assumption apparently isn't true.

The attack against the *cryptosystem*, as opposed to the attack against QM,
goes like this:  The eavesdropper clones the photons and SAVES them - he
makes no attempt to measure their polarization states yet.  Later, when Alice
has revealed to Bob (and the eavesdropper) which "regime" (circular or linear)
each photon polarization is to be measured in, the eavesdropper can safely go
back and measure just that state.  QM guarantees that he gets the same answers
Bob did, when Bob measured those same photons in Alice's "regime".  (On the
ones where Bob chose the wrong "regime", both the eavesdropper and Bob get
random answers.)  When Bob now tells Alice which photons he read in the
"right" regime, the eavesdropper learns which of his measurements to keep,
too.

Now, it's true that if Alice waits a while before revealing which measure-
ments to make, the eavesdropper will have trouble storing his photons.  But
that hardly seems fundamental; it's a question of technology.  Further, it's
essentially the same technology that Alice and Bob are relying on to transfer
the photons safely between them; so you'd have to be very careful here.

							-- Jerry