3,349 research outputs found
Exponential Separation of Quantum and Classical One-Way Communication Complexity for a Boolean Function
We give an exponential separation between one-way quantum and classical
communication complexity for a Boolean function. Earlier such a separation was
known only for a relation. A very similar result was obtained earlier but
independently by Kerenidis and Raz [KR06]. Our version of the result gives an
example in the bounded storage model of cryptography, where the key is secure
if the adversary has a certain amount of classical storage, but is completely
insecure if he has a similar amount of quantum storage.Comment: 8 pages, no 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
Tensor Norms and the Classical Communication Complexity of Nonlocal Quantum Measurement
We initiate the study of quantifying nonlocalness of a bipartite measurement
by the minimum amount of classical communication required to simulate the
measurement. We derive general upper bounds, which are expressed in terms of
certain tensor norms of the measurement operator. As applications, we show that
(a) If the amount of communication is constant, quantum and classical
communication protocols with unlimited amount of shared entanglement or shared
randomness compute the same set of functions; (b) A local hidden variable model
needs only a constant amount of communication to create, within an arbitrarily
small statistical distance, a distribution resulted from local measurements of
an entangled quantum state, as long as the number of measurement outcomes is
constant.Comment: A preliminary version of this paper appears as part of an article in
Proceedings of the the 37th ACM Symposium on Theory of Computing (STOC 2005),
460--467, 200
Exponential Separation of Quantum and Classical Online Space Complexity
Although quantum algorithms realizing an exponential time speed-up over the
best known classical algorithms exist, no quantum algorithm is known performing
computation using less space resources than classical algorithms. In this
paper, we study, for the first time explicitly, space-bounded quantum
algorithms for computational problems where the input is given not as a whole,
but bit by bit. We show that there exist such problems that a quantum computer
can solve using exponentially less work space than a classical computer. More
precisely, we introduce a very natural and simple model of a space-bounded
quantum online machine and prove an exponential separation of classical and
quantum online space complexity, in the bounded-error setting and for a total
language. The language we consider is inspired by a communication problem (the
set intersection function) that Buhrman, Cleve and Wigderson used to show an
almost quadratic separation of quantum and classical bounded-error
communication complexity. We prove that, in the framework of online space
complexity, the separation becomes exponential.Comment: 13 pages. v3: minor change
Exponential Separation of Quantum and Classical Non-Interactive Multi-Party Communication Complexity
We give the first exponential separation between quantum and classical
multi-party communication complexity in the (non-interactive) one-way and
simultaneous message passing settings.
For every k, we demonstrate a relational communication problem between k
parties that can be solved exactly by a quantum simultaneous message passing
protocol of cost O(log n) and requires protocols of cost n^{c/k^2}, where c>0
is a constant, in the classical non-interactive one-way message passing model
with shared randomness and bounded error.
Thus our separation of corresponding communication classes is superpolynomial
as long as k=o(\sqrt{\log n / \log\log n}) and exponential for k=O(1)
Quantum Cryptography Beyond Quantum Key Distribution
Quantum cryptography is the art and science of exploiting quantum mechanical
effects in order to perform cryptographic tasks. While the most well-known
example of this discipline is quantum key distribution (QKD), there exist many
other applications such as quantum money, randomness generation, secure two-
and multi-party computation and delegated quantum computation. Quantum
cryptography also studies the limitations and challenges resulting from quantum
adversaries---including the impossibility of quantum bit commitment, the
difficulty of quantum rewinding and the definition of quantum security models
for classical primitives. In this review article, aimed primarily at
cryptographers unfamiliar with the quantum world, we survey the area of
theoretical quantum cryptography, with an emphasis on the constructions and
limitations beyond the realm of QKD.Comment: 45 pages, over 245 reference
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