
10-year-old problem in theoretical computer science falls - maxko87
http://web.mit.edu/newsoffice/2012/interactive-proofs-work-even-if-quantum-information-is-used-0731.html
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anateus
To vastly (over?) simplify:

Interactive proofs can be used to prove you have a secret without divulging it
(<http://en.wikipedia.org/wiki/Zero_knowledge_proofs>) hence their mentioning
of crypto.

These systems can be attacked in various ways, one of which is to use quantum
entanglement. Edited to add: since the interactive proofs rely on
probabilistically estimating the likelihood respondents can still be lying,
quantum effects can be used to reduce the accuracy of these estimates. In this
case, entanglement is used as a means of collusion between supposedly
independent respondents.

What these researchers did was take an interactive proof that was already
created to be resilient against these quantum attacks , and have demonstrated
that it is in fact resilient against them.

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padobson
So me and my partner bust these two guys on a B&E on the wrong side of the
train tracks and haul their butts downtown to get confessions.

We separate 'em into to different rooms and really put the screws to 'em. We
musta questioned 'em for hours because the sludge coming out of the coffee pot
started to taste more like 10w30 than Folgers.

So these perps have all the answers, and we can't figure out how, because we
got a strong hunch we got these guys cold. So we figure they're using quantum
entanglement to keep their answers lined up. Each perp has his entangled
electron, spin it right for yes, left for no, and up for maybe. So we turn up
the heat and drop a Multi-prover interactive proof in their laps, and all of a
sudden their stories don't line up so well anymore.

Another hour of good-cop, bad-cop, and we get one perp to roll on the other.
Wasn't long till they were both singing like canaries and my partner and I had
a couple of fat collars.

A job well done.

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Xcelerate
If someone could translate that into English, that'd be great. I know a lot
about quantum physics, and a lot about computer science, but I still didn't
really understand what that was about. Although I did get excited.

~~~
thebooktocome
Have you tried looking up their paper? I normally can't glean very much from
popular press releases about mathematics either.

~~~
semenko
The paper is in the sidebar: <http://xxx.lanl.gov/abs/1207.0550>

""" We prove a strong limitation on the ability of entangled provers to
collude in a multiplayer game. Our main result is the first nontrivial lower
bound on the class MIP* of languages having multi-prover interactive proofs
with entangled provers; namely MIP* contains NEXP, the class of languages
decidable in non-deterministic exponential time. While Babai, Fortnow, and
Lund (Computational Complexity 1991) proved the celebrated equality MIP = NEXP
in the absence of entanglement, ever since the introduction of the class MIP*
it was open whether shared entanglement between the provers could weaken or
strengthen the computational power of multi-prover interactive proofs. Our
result shows that it does not weaken their computational power: MIP* contains
MIP. At the heart of our result is a proof that Babai, Fortnow, and Lund's
multilinearity test is sound even in the presence of entanglement between the
provers, and our analysis of this test could be of independent interest. As a
byproduct we show that the correlations produced by any entangled strategy
which succeeds in the multilinearity test with high probability can always be
closely approximated using shared randomness alone, and are thus restricted to
being quasi-classical. """

(I have no idea what that means.)

~~~
timtadh
I believe it says:

MIP = Multi-prover Interactive Proof, a class of languages, is known to be
equivalent to NEXP, (the class containing all languages computable in
exponential time by a machine operating in a non-deterministic fashion [eg.
the ones you care about]).

MIP* is like MIP except the provers (the M) are allowed to communicate with
each other using quantum entanglement. This type of communication would be
undetectable by the questioner (the verifier) and thus allow a group of
attackers to "cheat" various cryptographic protocols. However, it is found
that MIP* contains MIP. Therefore, there are proof systems (and thus
protocols) resistant to quantum communication of the provers.

Thus, zero-knowledge proofs and the like still work in with quantum
entanglement powered assailants.

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clvv
This video has a very good introduction to the problem.

<https://www.youtube.com/watch?v=eAiJocr6ZKg>

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philthom
I've studied computer science, but I don't recall this theoretical problem.
Perhaps its just not as popular or well known as things like P vs NP?

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nottaken
What are the implications of all this in other areas, fields and future of
humanity in general?

~~~
swordswinger12
It's an important result for post-quantum cryptography. If (when?) quantum
computers are ever generally deployable, existing ZK protocols with multiple
provers will need to be modified using this result. Besides, a theoretical
result doesn't need immediate applicability to be important to humanity. The
study of quadratic residues in Euler's time was a sort of mathematical
recreation, but 300 years later it gave us the QR hardness assumption and the
Goldwasser-Micali scheme and its derivatives.

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polynomial
Another triumph of mathematics over physics. /s

