12,834 research outputs found
Infinite Communication Complexity
Suppose that Alice and Bob are given each an infinite string, and they want
to decide whether their two strings are in a given relation. How much
communication do they need? How can communication be even defined and measured
for infinite strings? In this article, we propose a formalism for a notion of
infinite communication complexity, prove that it satisfies some natural
properties and coincides, for relevant applications, with the classical notion
of amortized communication complexity. More-over, an application is given for
tackling some conjecture about tilings and multidimensional sofic shifts.Comment: First Version. Written from the Computer Science PO
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
Is Communication Complexity Physical?
Recently, Brassard et. al. conjectured that the fact that the maximal
possible correlations between two non-local parties are the quantum-mechanical
ones is linked to a reasonable restriction on communication complexity. We
provide further support for the conjecture in the multipartite case. We show
that any multipartite communication complexity problem could be reduced to
triviality, had Nature been more non-local than quantum-mechanics by a quite
small gap for any number of parties. Intriguingly, the multipartite
nonlocal-box that we use to show the result corresponds to the generalized Bell
inequality that manifests maximal violation in respect to a local
hidden-variable theory
Communication Complexity of Cake Cutting
We study classic cake-cutting problems, but in discrete models rather than
using infinite-precision real values, specifically, focusing on their
communication complexity. Using general discrete simulations of classical
infinite-precision protocols (Robertson-Webb and moving-knife), we roughly
partition the various fair-allocation problems into 3 classes: "easy" (constant
number of rounds of logarithmic many bits), "medium" (poly-logarithmic total
communication), and "hard". Our main technical result concerns two of the
"medium" problems (perfect allocation for 2 players and equitable allocation
for any number of players) which we prove are not in the "easy" class. Our main
open problem is to separate the "hard" from the "medium" classes.Comment: Added efficient communication protocol for the monotone crossing
proble
Quantum Weakly Nondeterministic Communication Complexity
We study the weakest model of quantum nondeterminism in which a classical
proof has to be checked with probability one by a quantum protocol. We show the
first separation between classical nondeterministic communication complexity
and this model of quantum nondeterministic communication complexity for a total
function. This separation is quadratic.Comment: 12 pages. v3: minor correction
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
Quantum Entanglement and Communication Complexity
We consider a variation of the multi-party communication complexity scenario
where the parties are supplied with an extra resource: particles in an
entangled quantum state. We show that, although a prior quantum entanglement
cannot be used to simulate a communication channel, it can reduce the
communication complexity of functions in some cases. Specifically, we show
that, for a particular function among three parties (each of which possesses
part of the function's input), a prior quantum entanglement enables them to
learn the value of the function with only three bits of communication occurring
among the parties, whereas, without quantum entanglement, four bits of
communication are necessary. We also show that, for a particular two-party
probabilistic communication complexity problem, quantum entanglement results in
less communication than is required with only classical random correlations
(instead of quantum entanglement). These results are a noteworthy contrast to
the well-known fact that quantum entanglement cannot be used to actually
simulate communication among remote parties.Comment: 10 pages, latex, no figure
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