813 research outputs found
Quantum Communication Cannot Simulate a Public Coin
We study the simultaneous message passing model of communication complexity.
Building on the quantum fingerprinting protocol of Buhrman et al., Yao recently
showed that a large class of efficient classical public-coin protocols can be
turned into efficient quantum protocols without public coin. This raises the
question whether this can be done always, i.e. whether quantum communication
can always replace a public coin in the SMP model. We answer this question in
the negative, exhibiting a communication problem where classical communication
with public coin is exponentially more efficient than quantum communication.
Together with a separation in the other direction due to Bar-Yossef et al.,
this shows that the quantum SMP model is incomparable with the classical
public-coin SMP model.
In addition we give a characterization of the power of quantum fingerprinting
by means of a connection to geometrical tools from machine learning, a
quadratic improvement of Yao's simulation, and a nearly tight analysis of the
Hamming distance problem from Yao's paper.Comment: 12 pages LaTe
Strengths and Weaknesses of Quantum Fingerprinting
We study the power of quantum fingerprints in the simultaneous message
passing (SMP) setting of communication complexity. Yao recently showed how to
simulate, with exponential overhead, classical shared-randomness SMP protocols
by means of quantum SMP protocols without shared randomness
(-protocols). Our first result is to extend Yao's simulation to
the strongest possible model: every many-round quantum protocol with unlimited
shared entanglement can be simulated, with exponential overhead, by
-protocols. We apply our technique to obtain an efficient
-protocol for a function which cannot be efficiently solved
through more restricted simulations. Second, we tightly characterize the power
of the quantum fingerprinting technique by making a connection to arrangements
of homogeneous halfspaces with maximal margin. These arrangements have been
well studied in computational learning theory, and we use some strong results
obtained in this area to exhibit weaknesses of quantum fingerprinting. In
particular, this implies that for almost all functions, quantum fingerprinting
protocols are exponentially worse than classical deterministic SMP protocols.Comment: 13 pages, no figures, to appear in CCC'0
New Bounds for the Garden-Hose Model
We show new results about the garden-hose model. Our main results include
improved lower bounds based on non-deterministic communication complexity
(leading to the previously unknown bounds for Inner Product mod 2
and Disjointness), as well as an upper bound for the
Distributed Majority function (previously conjectured to have quadratic
complexity). We show an efficient simulation of formulae made of AND, OR, XOR
gates in the garden-hose model, which implies that lower bounds on the
garden-hose complexity of the order will be
hard to obtain for explicit functions. Furthermore we study a time-bounded
variant of the model, in which even modest savings in time can lead to
exponential lower bounds on the size of garden-hose protocols.Comment: In FSTTCS 201
Efficient quantum protocols for XOR functions
We show that for any Boolean function f on {0,1}^n, the bounded-error quantum
communication complexity of XOR functions satisfies that
, where d is the F2-degree of f, and
.
This implies that the previous lower bound by Lee and Shraibman \cite{LS09} is tight
for f with low F2-degree. The result also confirms the quantum version of the
Log-rank Conjecture for low-degree XOR functions. In addition, we show that the
exact quantum communication complexity satisfies , where is the number of nonzero Fourier coefficients of
f. This matches the previous lower bound
by Buhrman and de Wolf \cite{BdW01} for low-degree XOR functions.Comment: 11 pages, no figur
Concurrently Non-Malleable Zero Knowledge in the Authenticated Public-Key Model
We consider a type of zero-knowledge protocols that are of interest for their
practical applications within networks like the Internet: efficient
zero-knowledge arguments of knowledge that remain secure against concurrent
man-in-the-middle attacks. In an effort to reduce the setup assumptions
required for efficient zero-knowledge arguments of knowledge that remain secure
against concurrent man-in-the-middle attacks, we consider a model, which we
call the Authenticated Public-Key (APK) model. The APK model seems to
significantly reduce the setup assumptions made by the CRS model (as no trusted
party or honest execution of a centralized algorithm are required), and can be
seen as a slightly stronger variation of the Bare Public-Key (BPK) model from
\cite{CGGM,MR}, and a weaker variation of the registered public-key model used
in \cite{BCNP}. We then define and study man-in-the-middle attacks in the APK
model. Our main result is a constant-round concurrent non-malleable
zero-knowledge argument of knowledge for any polynomial-time relation
(associated to a language in ), under the (minimal) assumption of
the existence of a one-way function family. Furthermore,We show time-efficient
instantiations of our protocol based on known number-theoretic assumptions. We
also note a negative result with respect to further reducing the setup
assumptions of our protocol to those in the (unauthenticated) BPK model, by
showing that concurrently non-malleable zero-knowledge arguments of knowledge
in the BPK model are only possible for trivial languages
Non-locality and Communication Complexity
Quantum information processing is the emerging field that defines and
realizes computing devices that make use of quantum mechanical principles, like
the superposition principle, entanglement, and interference. In this review we
study the information counterpart of computing. The abstract form of the
distributed computing setting is called communication complexity. It studies
the amount of information, in terms of bits or in our case qubits, that two
spatially separated computing devices need to exchange in order to perform some
computational task. Surprisingly, quantum mechanics can be used to obtain
dramatic advantages for such tasks.
We review the area of quantum communication complexity, and show how it
connects the foundational physics questions regarding non-locality with those
of communication complexity studied in theoretical computer science. The first
examples exhibiting the advantage of the use of qubits in distributed
information-processing tasks were based on non-locality tests. However, by now
the field has produced strong and interesting quantum protocols and algorithms
of its own that demonstrate that entanglement, although it cannot be used to
replace communication, can be used to reduce the communication exponentially.
In turn, these new advances yield a new outlook on the foundations of physics,
and could even yield new proposals for experiments that test the foundations of
physics.Comment: Survey paper, 63 pages LaTeX. A reformatted version will appear in
Reviews of Modern Physic
Classical Cryptographic Protocols in a Quantum World
Cryptographic protocols, such as protocols for secure function evaluation
(SFE), have played a crucial role in the development of modern cryptography.
The extensive theory of these protocols, however, deals almost exclusively with
classical attackers. If we accept that quantum information processing is the
most realistic model of physically feasible computation, then we must ask: what
classical protocols remain secure against quantum attackers?
Our main contribution is showing the existence of classical two-party
protocols for the secure evaluation of any polynomial-time function under
reasonable computational assumptions (for example, it suffices that the
learning with errors problem be hard for quantum polynomial time). Our result
shows that the basic two-party feasibility picture from classical cryptography
remains unchanged in a quantum world.Comment: Full version of an old paper in Crypto'11. Invited to IJQI. This is
authors' copy with different formattin
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