Can Eve repeat?

[Peter Fairbrother]

Dan Riley wrote:

> I'm not an expert on this stuff, but I'm interested enough to chase
> a few references...
> 
> Ivan Krstic <ccikrs1 at cranbrook.edu> writes:
>> 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.
> 
> Careful there--EV interaction-free measurements do *not* read the
> internal state of the system measured.  The trick to the EV IFM is
> that it determines the location (or existence) of a system without
> interacting with the internal state of that system; a corollary is
> that it derives no information about the internal state.

Caveat - I'm slightly drunk, and in a quitting-nicotine state...

IFM's can detect classical measurements, without changing the classical
measurement (eg the presence of an obstacle in a path). They may change the
quantum state of the classical measurement, but that doesn't matter as far
as changing it's classical aspect goes.


What I was referring to was using IFM and quantum Zeno techniques to detect
_which_ quanta were incorrectly cloned by a UQCM. That would increase the
Shannon information available to Eve, and allow her to either stop
transmission of the incorrectly cloned quanta, or, and this is an unknown
step, to reconstruct the incident quantum and try again to clone it.

The simple apparatus is just a UQCM in one limb of a Mach-Zender
interferometer. That's enough to increase Eve's Shannon infomation. The QZ
apparatus I can't describe, but I can well imagine one that would allow
near-perfect detection of incorrect clones.


> "The meaning of the EV IFM is that if an object changes its internal
> state [...] due to the radiation, then the method allows detection
> of the location of the object without any change in its internal
> state.
> [...]
> We should mention that the interaction-free measurements do not
> have vanishing interaction Hamiltonian. [...] the IFM can change
> very significantly the quantum state of the observed object and we
> still name it interaction free."
> Lev Vaidman, "Are Interaction-free Measurements Interaction
> Free?", http://arxiv.org/abs/quant-ph/0006077

But this follows your quote:

"On the other hand the method do allow performing some non-demolition
measurements. It might be momentum-exchange free and energy-exchange free."

You are claiming too much, and ignoring what the paper actually says. Bad
boy! Spank! It might be changing-polarisation-free too. I'm pretty sure it
can be.


> Intercepting QC is all about determining the internal state (e.g.
> photon polarization), and AFAIK that requires becoming entangled with
> the state of the particle.  EV IFM doesn't appear to provide a way
> around this.

Not entirely. IFM techniques can also eg compare the incident photon with
the same photon in a "has-been-cloned" state. The theory is slightly
different, which was why I said "sort of" in my earlier post on the subject.

> and later...
>> On Fri, 26 Sep 2003 09:10:05 -0400, Greg Troxel <gdt at ir.bbn.com> wrote:
>>> The current canoncial
>>> paper on how to calculate the number of bits that must be hashed away
>>> due to detected eavesdropping and the inferred amount of undetected
>>> eavesdropping is "Defense frontier analysis of quantum cryptographic
>>> systems" by Slutsky et al:
>>> 
>>> http://topaz.ucsd.edu/papers/defense.pdf
>> 
>> Up-front disclaimer: I haven't had time to study this paper with the
>> level of attention it likely deserves, so I apologize if the following
>> contains incorrect logic. However, from glancing over it, it appears
>> the assumptions on which the entire paper rests are undermined by work
>> such as that of Elitzur and Vaidman (see the article I linked
>> previously). Specifically, note the following:
> [...]
>> If we do away with the idea that there are no interaction-free
>> measurements (which was, at least to me, convincingly shown by the
>> Quantum seeing in the dark article), this paper becomes considerably
>> less useful; the first claim's validity is completely nullified (no
>> longer does interference with particles necessarily introduce
>> transmission errors),
> 
> If Eve can measure the state of a particle without altering its state
> at all, 100% of the time, then QC is dead--the defense function
> becomes infinite.  But AFAICT the EV IFM techniques do not provide
> this ability.

Not as you describe. But the earlier "it would defy Einsteinian causality"
(without a detailed explanation of how) argument has been shown to be wrong,
and there is now nothing I know of that will prevent EV IFM-like techniques
working to detect which quanta are incorrectly cloned. Or recreating the
original photon (though there might be limits on that).


>> while the effect on the second statement is
>> evil: employing the proposed key distillation techniques, the user
>> might be given a (very) false sense of security, as only a small
>> percentage of the particles that Eve observes register as transmission
>> errors (<=15%, according to the LANL figure).
> 
> Err...I think you've missed the point of the paper.  What they're
> doing is deriving how many extra bits Alice and Bob have to transmit
> given that Eve is intercepting their transmission, and only some
> fraction (dependent on the interception technique) of those
> interceptions are detectable.  They do not assume that all
> interceptions appear as errors; they (initially) assume that all
> errors are due to interceptions (they deal with the case of noisy
> channels later in the paper).

Yep. Nope. Maybe. I forget what the second statement was. I've got a feeling
that Ivan had a point tho'.

:)

-- 
Peter

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