64 research outputs found
A large family of quantum weak coin-flipping protocols
Each classical public-coin protocol for coin flipping is naturally associated
with a quantum protocol for weak coin flipping. The quantum protocol is
obtained by replacing classical randomness with quantum entanglement and by
adding a cheat detection test in the last round that verifies the integrity of
this entanglement. The set of such protocols defines a family which contains
the protocol with bias 0.192 previously found by the author, as well as
protocols with bias as low as 1/6 described herein. The family is analyzed by
identifying a set of optimal protocols for every number of messages. In the
end, tight lower bounds for the bias are obtained which prove that 1/6 is
optimal for all protocols within the family.Comment: 17 pages, REVTeX 4 (minor corrections in v2
Multiparty Quantum Coin Flipping
We investigate coin-flipping protocols for multiple parties in a quantum
broadcast setting:
(1) We propose and motivate a definition for quantum broadcast. Our model of
quantum broadcast channel is new.
(2) We discovered that quantum broadcast is essentially a combination of
pairwise quantum channels and a classical broadcast channel. This is a somewhat
surprising conclusion, but helps us in both our lower and upper bounds.
(3) We provide tight upper and lower bounds on the optimal bias epsilon of a
coin which can be flipped by k parties of which exactly g parties are honest:
for any 1 <= g <= k, epsilon = 1/2 - Theta(g/k).
Thus, as long as a constant fraction of the players are honest, they can
prevent the coin from being fixed with at least a constant probability. This
result stands in sharp contrast with the classical setting, where no
non-trivial coin-flipping is possible when g <= k/2.Comment: v2: bounds now tight via new protocol; to appear at IEEE Conference
on Computational Complexity 200
Tight bounds for classical and quantum coin flipping
Coin flipping is a cryptographic primitive for which strictly better
protocols exist if the players are not only allowed to exchange classical, but
also quantum messages. During the past few years, several results have appeared
which give a tight bound on the range of implementable unconditionally secure
coin flips, both in the classical as well as in the quantum setting and for
both weak as well as strong coin flipping. But the picture is still incomplete:
in the quantum setting, all results consider only protocols with perfect
correctness, and in the classical setting tight bounds for strong coin flipping
are still missing. We give a general definition of coin flipping which unifies
the notion of strong and weak coin flipping (it contains both of them as
special cases) and allows the honest players to abort with a certain
probability. We give tight bounds on the achievable range of parameters both in
the classical and in the quantum setting.Comment: 18 pages, 2 figures; v2: published versio
Toward a general theory of quantum games
We study properties of quantum strategies, which are complete specifications
of a given party's actions in any multiple-round interaction involving the
exchange of quantum information with one or more other parties. In particular,
we focus on a representation of quantum strategies that generalizes the
Choi-Jamio{\l}kowski representation of quantum operations. This new
representation associates with each strategy a positive semidefinite operator
acting only on the tensor product of its input and output spaces. Various facts
about such representations are established, and two applications are discussed:
the first is a new and conceptually simple proof of Kitaev's lower bound for
strong coin-flipping, and the second is a proof of the exact characterization
QRG = EXP of the class of problems having quantum refereed games.Comment: 23 pages, 12pt font, single-column compilation of STOC 2007 final
versio
Unconditionally secure quantum coin flipping
Quantum coin flipping (QCF) is an essential primitive for quantum
cryptography. Unconditionally secure strong QCF with an arbitrarily small bias
was widely believed to be impossible. But basing on a problem which cannot be
solved without quantum algorithm, here we propose such a QCF protocol, and show
how it manages to evade all existing no-go proofs on QCF.Comment: The protocol is modified so that the security proof can be
simplified. Also corrected a flaw in the analysis on the no-go proof in
Ref.[13]. We thank the anonymous referee for pinpointing out the fla
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