Date: Thu, 4 Nov 2010 01:12:50 +0100 (CET)
From: Vadim Makarov <makarov@vad1.com>
To: Vojtech Hala <egg@matfyz.cz>
Subject: Re: Cloning by stimmulated emission

On Wed, 3 Nov 2010, Vojtech Hala wrote:
> Dear Dr. Makarov,
>
> I'm a high-school teacher and I'm curious about almost everything that goes on
> in science and especially quantum information processing. That includes the
> research done by the Quantum Hacking group. I have an idea about QKD which I
> wasn't able to confirm in literature or Internet.
>
> The no-cloning theorem of quantum mechanics should prevent Eve from copying
> unkwnown polarization states transmitted from Alice to Bob and then reading
> the copies. On the other hand the photon created by stimmulated emission is
> expected to be in (almost) exactly the same state as the initial one since
> they are bosons. That seems to be a contrary. My question is whether the BB84
> protocol (which doesn't involve entanglement) is vulnerable to copying photons
> by stimmulated emission. Of course the fidelity is not 100% but I still think
> that with a piece of dexterity the presence of Eve would appear to be just a
> little noise on the line. Using stuff like this... why not?
> http://www.sciencemag.org/cgi/content/abstract/296/5568/712
> http://www.photonics.com/Article.aspx?AID=12923
>
> Is it a good idea worth of a try or am I wrong?
>
> Thank you and good luck with your research!
>
> Sincerely,
>
> --
> Vojtěch Hála (aka Egg)

Hi Vojtěch,

The abstract at the 1st link actually says it quite clearly, except that a
reader may (understandably) be confused by a bit unfortunate terminology
accepted in this field of physics. When they say "optimal fidelity", it
means "fidelity at a certain value notably less than 1, which is the best
that can be achieved".

In quantum cryptography, we know that the eavesdropper can only do as well
as this less than unity fidelity value. Thus an eavesdropper introduces a
certain minimum fraction of errors in the key, a value notably above zero.
The legitimate parties sacrify a part of their key to check how big the
actual fraction of errors is in the key, and abort the communication if it
exceeds the above value.

Now, you are right that real lines always have a bit of noise, even if
nobody eavesdrops. Quantum cryptographic protocols deal with this noise:
If the error fraction is non-zero but below the abovementioned value, then
distillation of a shorter secret key is possibly by mathematical technique
called "privacy amplification". The cut-off error fraction is
approximately 11%; below it the eavesdropper in principle cannot have full
information, and distillation of secret key is possible by the legitimate
parties.

Vadim