85,563 research outputs found
New Separations Results for External Information
We obtain new separation results for the two-party external information
complexity of boolean functions. The external information complexity of a
function is the minimum amount of information a two-party protocol
computing must reveal to an outside observer about the input. We obtain the
following results:
1. We prove an exponential separation between external and internal
information complexity, which is the best possible; previously no separation
was known.
2. We prove a near-quadratic separation between amortized zero-error
communication complexity and external information complexity for total
functions, disproving a conjecture of \cite{Bravermansurvey}.
3. We prove a matching upper showing that our separation result is tight
Exponential Separation of Quantum Communication and Classical Information
We exhibit a Boolean function for which the quantum communication complexity
is exponentially larger than the classical information complexity. An
exponential separation in the other direction was already known from the work
of Kerenidis et. al. [SICOMP 44, pp. 1550-1572], hence our work implies that
these two complexity measures are incomparable. As classical information
complexity is an upper bound on quantum information complexity, which in turn
is equal to amortized quantum communication complexity, our work implies that a
tight direct sum result for distributional quantum communication complexity
cannot hold. The function we use to present such a separation is the Symmetric
k-ary Pointer Jumping function introduced by Rao and Sinha [ECCC TR15-057],
whose classical communication complexity is exponentially larger than its
classical information complexity. In this paper, we show that the quantum
communication complexity of this function is polynomially equivalent to its
classical communication complexity. The high-level idea behind our proof is
arguably the simplest so far for such an exponential separation between
information and communication, driven by a sequence of round-elimination
arguments, allowing us to simplify further the approach of Rao and Sinha.
As another application of the techniques that we develop, we give a simple
proof for an optimal trade-off between Alice's and Bob's communication while
computing the related Greater-Than function on n bits: say Bob communicates at
most b bits, then Alice must send n/exp(O(b)) bits to Bob. This holds even when
allowing pre-shared entanglement. We also present a classical protocol
achieving this bound.Comment: v1, 36 pages, 3 figure
Experimental Quantum Fingerprinting
Quantum communication holds the promise of creating disruptive technologies
that will play an essential role in future communication networks. For example,
the study of quantum communication complexity has shown that quantum
communication allows exponential reductions in the information that must be
transmitted to solve distributed computational tasks. Recently, protocols that
realize this advantage using optical implementations have been proposed. Here
we report a proof of concept experimental demonstration of a quantum
fingerprinting system that is capable of transmitting less information than the
best known classical protocol. Our implementation is based on a modified
version of a commercial quantum key distribution system using off-the-shelf
optical components over telecom wavelengths, and is practical for messages as
large as 100 Mbits, even in the presence of experimental imperfections. Our
results provide a first step in the development of experimental quantum
communication complexity.Comment: 11 pages, 6 Figure
Partition bound is quadratically tight for product distributions
Let be a 2-party
function. For every product distribution on ,
we show that
where is the distributional communication
complexity of with error at most under the distribution
and is the {\em partition bound} of , as defined by
Jain and Klauck [{\em Proc. 25th CCC}, 2010]. We also prove a similar bound in
terms of , the {\em information complexity} of ,
namely, The latter bound was recently and
independently established by Kol [{\em Proc. 48th STOC}, 2016] using a
different technique.
We show a similar result for query complexity under product distributions.
Let be a function. For every bit-wise
product distribution on , we show that
where
is the distributional query complexity of
with error at most under the distribution and
is the {\em query partition bound} of the function
.
Partition bounds were introduced (in both communication complexity and query
complexity models) to provide LP-based lower bounds for randomized
communication complexity and randomized query complexity. Our results
demonstrate that these lower bounds are polynomially tight for {\em product}
distributions.Comment: The previous version of the paper erroneously stated the main result
in terms of relaxed partition number instead of partition numbe
Improving Receiver Performance of Diffusive Molecular Communication with Enzymes
This paper studies the mitigation of intersymbol interference in a diffusive
molecular communication system using enzymes that freely diffuse in the
propagation environment. The enzymes form reaction intermediates with
information molecules and then degrade them so that they cannot interfere with
future transmissions. A lower bound expression on the expected number of
molecules measured at the receiver is derived. A simple binary receiver
detection scheme is proposed where the number of observed molecules is sampled
at the time when the maximum number of molecules is expected. Insight is also
provided into the selection of an appropriate bit interval. The expected bit
error probability is derived as a function of the current and all previously
transmitted bits. Simulation results show the accuracy of the bit error
probability expression and the improvement in communication performance by
having active enzymes present.Comment: 13 pages, 8 figures, 1 table. To appear in IEEE Transactions on
Nanobioscience (submitted January 22, 2013; minor revision October 16, 2013;
accepted December 4, 2013
Quantum Energy Teleportation with Electromagnetic Field: Discrete vs. Continuous Variables
It is well known that usual quantum teleportation protocols cannot transport
energy. Recently, new protocols called quantum energy teleportation (QET) have
been proposed, which transport energy by local operations and classical
communication with the ground states of many-body quantum systems. In this
paper, we compare two different QET protocols for transporting energy with
electromagnetic field. In the first protocol, a 1/2 spin (a qubit) is coupled
with the quantum fluctuation in the vacuum state and measured in order to
obtain one-bit information about the fluctuation for the teleportation. In the
second protocol, a harmonic oscillator is coupled with the fluctuation and
measured in order to obtain continuous-variable information about the
fluctuation. In the spin protocol, the amount of teleported energy is
suppressed by an exponential damping factor when the amount of input energy
increases. This suppression factor becomes power damping in the case of the
harmonic oscillator protocol. Therefore, it is concluded that obtaining more
information about the quantum fluctuation leads to teleporting more energy.
This result suggests a profound relationship between energy and quantum
information.Comment: 24 pages, 4 figures, to be published in Journal of Physics A:
Mathematical and Theoretica
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