18,736 research outputs found
Quantum linear network coding as one-way quantum computation
Network coding is a technique to maximize communication rates within a
network, in communication protocols for simultaneous multi-party transmission
of information. Linear network codes are examples of such protocols in which
the local computations performed at the nodes in the network are limited to
linear transformations of their input data (represented as elements of a ring,
such as the integers modulo 2). The quantum linear network coding protocols of
Kobayashi et al [arXiv:0908.1457 and arXiv:1012.4583] coherently simulate
classical linear network codes, using supplemental classical communication. We
demonstrate that these protocols correspond in a natural way to
measurement-based quantum computations with graph states over over qudits
[arXiv:quant-ph/0301052, arXiv:quant-ph/0603226, and arXiv:0704.1263] having a
structure directly related to the network.Comment: 17 pages, 6 figures. Updated to correct an incorrect (albeit
hilarious) reference in the arXiv version of the abstrac
General Scheme for Perfect Quantum Network Coding with Free Classical Communication
This paper considers the problem of efficiently transmitting quantum states
through a network. It has been known for some time that without additional
assumptions it is impossible to achieve this task perfectly in general --
indeed, it is impossible even for the simple butterfly network. As additional
resource we allow free classical communication between any pair of network
nodes. It is shown that perfect quantum network coding is achievable in this
model whenever classical network coding is possible over the same network when
replacing all quantum capacities by classical capacities. More precisely, it is
proved that perfect quantum network coding using free classical communication
is possible over a network with source-target pairs if there exists a
classical linear (or even vector linear) coding scheme over a finite ring. Our
proof is constructive in that we give explicit quantum coding operations for
each network node. This paper also gives an upper bound on the number of
classical communication required in terms of , the maximal fan-in of any
network node, and the size of the network.Comment: 12 pages, 2 figures, generalizes some of the results in
arXiv:0902.1299 to the k-pair problem and codes over rings. Appeared in the
Proceedings of the 36th International Colloquium on Automata, Languages and
Programming (ICALP'09), LNCS 5555, pp. 622-633, 200
Quantum Capacities for Entanglement Networks
We discuss quantum capacities for two types of entanglement networks:
for the quantum repeater network with free classical
communication, and for the tensor network as the rank of the
linear operation represented by the tensor network. We find that
always equals in the regularized case for the samenetwork graph.
However, the relationships between the corresponding one-shot capacities
and are more complicated, and the min-cut upper
bound is in general not achievable. We show that the tensor network can be
viewed as a stochastic protocol with the quantum repeater network, such that
is a natural upper bound of . We analyze the
possible gap between and for certain networks,
and compare them with the one-shot classical capacity of the corresponding
classical network
Experimental quantum coding against photon loss error
A significant obstacle for practical quantum computation is the loss of
physical qubits in quantum computers, a decoherence mechanism most notably in
optical systems. Here we experimentally demonstrate, both in the quantum
circuit model and in the one-way quantum computer model, the smallest
non-trivial quantum codes to tackle this problem. In the experiment, we encode
single-qubit input states into highly-entangled multiparticle codewords, and we
test their ability to protect encoded quantum information from detected
one-qubit loss error. Our results prove the in-principle feasibility of
overcoming the qubit loss error by quantum codes.Comment: "Quantum Computing even when Photons Go AWOL". published versio
A very brief introduction to quantum computing and quantum information theory for mathematicians
This is a very brief introduction to quantum computing and quantum
information theory, primarily aimed at geometers. Beyond basic definitions and
examples, I emphasize aspects of interest to geometers, especially connections
with asymptotic representation theory. Proofs of most statements can be found
in standard references
Spin network quantum simulator
We propose a general setting for a universal representation of the quantum
structure on which quantum information stands, whose dynamical evolution
(information manipulation) is based on angular momentum recoupling theory. Such
scheme complies with the notion of 'quantum simulator' in the sense of
Feynmann, and is shown to be related with the topological quantum field theory
approach to quantum computation.Comment: revtex, 6 pages + 5 figure
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