721 research outputs found
Complete Insecurity of Quantum Protocols for Classical Two-Party Computation
A fundamental task in modern cryptography is the joint computation of a
function which has two inputs, one from Alice and one from Bob, such that
neither of the two can learn more about the other's input than what is implied
by the value of the function. In this Letter, we show that any quantum protocol
for the computation of a classical deterministic function that outputs the
result to both parties (two-sided computation) and that is secure against a
cheating Bob can be completely broken by a cheating Alice. Whereas it is known
that quantum protocols for this task cannot be completely secure, our result
implies that security for one party implies complete insecurity for the other.
Our findings stand in stark contrast to recent protocols for weak coin tossing,
and highlight the limits of cryptography within quantum mechanics. We remark
that our conclusions remain valid, even if security is only required to be
approximate and if the function that is computed for Bob is different from that
of Alice.Comment: v2: 6 pages, 1 figure, text identical to PRL-version (but reasonably
formatted
Quantum to Classical Randomness Extractors
The goal of randomness extraction is to distill (almost) perfect randomness
from a weak source of randomness. When the source yields a classical string X,
many extractor constructions are known. Yet, when considering a physical
randomness source, X is itself ultimately the result of a measurement on an
underlying quantum system. When characterizing the power of a source to supply
randomness it is hence a natural question to ask, how much classical randomness
we can extract from a quantum system. To tackle this question we here take on
the study of quantum-to-classical randomness extractors (QC-extractors). We
provide constructions of QC-extractors based on measurements in a full set of
mutually unbiased bases (MUBs), and certain single qubit measurements. As the
first application, we show that any QC-extractor gives rise to entropic
uncertainty relations with respect to quantum side information. Such relations
were previously only known for two measurements. As the second application, we
resolve the central open question in the noisy-storage model [Wehner et al.,
PRL 100, 220502 (2008)] by linking security to the quantum capacity of the
adversary's storage device.Comment: 6+31 pages, 2 tables, 1 figure, v2: improved converse parameters,
typos corrected, new discussion, v3: new reference
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