795 research outputs found
Experimental quantum communication complexity
We prove that the fidelity of two exemplary communication complexity
protocols, allowing for an N-1 bit communication, can be exponentially improved
by N-1 (unentangled) qubit communication. Taking into account, for a fair
comparison, all inefficiencies of state-of-the-art set-up, the experimental
implementation outperforms the best classical protocol, making it the candidate
for multi-party quantum communication applications.Comment: 4 pages, 2 eps figures, RevTEX4; submitted June 23, 200
Quantum communication complexity of symmetric predicates
We completely (that is, up to a logarithmic factor) characterize the
bounded-error quantum communication complexity of every predicate
depending only on (). Namely, for a predicate
on let \ell_0(D)\df \max\{\ell : 1\leq\ell\leq n/2\land
D(\ell)\not\equiv D(\ell-1)\} and \ell_1(D)\df \max\{n-\ell : n/2\leq\ell <
n\land D(\ell)\not\equiv D(\ell+1)\}. Then the bounded-error quantum
communication complexity of is equal (again, up to a
logarithmic factor) to . In particular, the
complexity of the set disjointness predicate is . This result
holds both in the model with prior entanglement and without it.Comment: 20 page
The quantum communication complexity of sampling
Sampling is an important primitive in probabilistic and quantum algorithms. In the spirit of communication complexity, given a function f : X × Y → {0, 1} and a probability distribution D over X × Y , we define the sampling complexity of (f,D) as the minimum number of bits that Alice and Bob must communicate for Alice to pick x ∈ X and Bob to pick y ∈ Y as well as a value z such that the resulting distribution of (x, y, z) is close to the distribution (D, f(D)).
In this paper we initiate the study of sampling complexity, in both the classical and quantum models. We give several variants of a definition. We completely characterize some of these variants and give upper and lower bounds on others. In particular, this allows us to establish an exponential gap between quantum and classical sampling complexity for the set-disjointness function
Unbounded-Error Classical and Quantum Communication Complexity
Since the seminal work of Paturi and Simon \cite[FOCS'84 & JCSS'86]{PS86},
the unbounded-error classical communication complexity of a Boolean function
has been studied based on the arrangement of points and hyperplanes. Recently,
\cite[ICALP'07]{INRY07} found that the unbounded-error {\em quantum}
communication complexity in the {\em one-way communication} model can also be
investigated using the arrangement, and showed that it is exactly (without a
difference of even one qubit) half of the classical one-way communication
complexity. In this paper, we extend the arrangement argument to the {\em
two-way} and {\em simultaneous message passing} (SMP) models. As a result, we
show similarly tight bounds of the unbounded-error two-way/one-way/SMP
quantum/classical communication complexities for {\em any} partial/total
Boolean function, implying that all of them are equivalent up to a
multiplicative constant of four. Moreover, the arrangement argument is also
used to show that the gap between {\em weakly} unbounded-error quantum and
classical communication complexities is at most a factor of three.Comment: 11 pages. To appear at Proc. ISAAC 200
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