Can Eve repeat?

[Peter Fairbrother]

Ivan Krstic wrote:

> On 24 Sep 2003 08:34:57 -0400, Greg Troxel <gdt at ir.bbn.com> wrote:
> [snip]
>> In Quantum Cryptography, Eve is allowed to not only observe, but also
>> transmit (in the quantum world observing modifies state, so the notion
>> of read only doesn't make sense).  Also, Eve is typically accorded
>> unlimited computational power.
> [snip]
> 
> The idea that observing modifies state is something to be approached with
> caution. Read-only does make sense in quantum world; implementations of
> early theoretical work by Elitzur and Vaidman achieved roughly 50% success
> on interaction-free measurements. Later work, relying on the quantum Zeno
> effect, raised the success rate significantly: "Preliminary results from
> new experiments at Los Alamos National Laboratory have demonstrated that
> up to 70 percent of measurements could be interaction-free. We soon hope
> to increase that figure to 85 percent."
> 
> The quote comes from a article by Kwiat, Weinfurter and Zeilinger
> published in SciAm, November 1996 -- if they were getting success rates
> like these back then, I wonder what the current status is.
> 
> The article is well worth a read. There's a copy online at:
> http://www.fortunecity.com/emachines/e11/86/seedark.html
> 
> Best regards,
> Ivan Krstic

Thanks for the interesting link.

That's pretty much what I was talking about when I said that it may be
possible to clone an arbitrarily large proportion of photons - and that
Quantum Cryptography may not actually be secure.

For instance, you can clone a "virtual" photon and do an interaction-free
measurement comparing the now-cloned photon and the photon in it's uncloned
state. If they don't match, the photon was incorrectly cloned. You may only
be able to correctly clone 5/6 of the photons, but that way you know which
photons were correctly cloned.

It may also be possible to clone an arbitrarily large proportion of photons,
ie approaching all of them, by measuring the incorrectly cloned photons and
their clones or transforming to get the original photon back, then trying to
clone again. Other methods are perhaps possible too.


The "no-cloning rule" says that no unitary transform will take two quantum
waveforms, one unknown, and generate two wavefoms with the same state as the
unknown waveform. It's probably true (anent some non-linear transform), but
it _doesn't_ say that there isn't another way to clone quanta, perhaps using
three waveforms, or "virtual" waveforms, or generating a new quantum from
interaction-free measurement of the original quantum waveform.

IMO far too much reliance has been placed on it, or perhaps people just
misunderstood what it says.


It reminds me a bit of the "cd's are better than vinyl" dispute - the cd
guys said that Nyquist theorem showed that cd's reproduced music to above
human hearing, but it doesn't, it just shows that less-than-Nyquist sampling
rates have extra problems. And it only applies to steady states, not music.
And so on.

And the "no-cloning rule" _doesn't_ say it's impossible to clone. Perhaps it
should be called somthing else.


-- 
Peter Fairbrother

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