1,158 research outputs found
Enhanced Feedback Iterative Decoding of Sparse Quantum Codes
Decoding sparse quantum codes can be accomplished by syndrome-based decoding
using a belief propagation (BP) algorithm.We significantly improve this
decoding scheme by developing a new feedback adjustment strategy for the
standard BP algorithm. In our feedback procedure, we exploit much of the
information from stabilizers, not just the syndrome but also the values of the
frustrated checks on individual qubits of the code and the channel model.
Furthermore we show that our decoding algorithm is superior to belief
propagation algorithms using only the syndrome in the feedback procedure for
all cases of the depolarizing channel. Our algorithm does not increase the
measurement overhead compared to the previous method, as the extra information
comes for free from the requisite stabilizer measurements.Comment: 10 pages, 11 figures, Second version, To be appeared in IEEE
Transactions on Information Theor
Quantum channels and their entropic characteristics
One of the major achievements of the recently emerged quantum information
theory is the introduction and thorough investigation of the notion of quantum
channel which is a basic building block of any data-transmitting or
data-processing system. This development resulted in an elaborated structural
theory and was accompanied by the discovery of a whole spectrum of entropic
quantities, notably the channel capacities, characterizing
information-processing performance of the channels. This paper gives a survey
of the main properties of quantum channels and of their entropic
characterization, with a variety of examples for finite dimensional quantum
systems. We also touch upon the "continuous-variables" case, which provides an
arena for quantum Gaussian systems. Most of the practical realizations of
quantum information processing were implemented in such systems, in particular
based on principles of quantum optics. Several important entropic quantities
are introduced and used to describe the basic channel capacity formulas. The
remarkable role of the specific quantum correlations - entanglement - as a
novel communication resource, is stressed.Comment: review article, 60 pages, 5 figures, 194 references; Rep. Prog. Phys.
(in press
Entanglement Transfer Through an Antiferromagnetic Spin Chain
We study the possibility of using an uniformly coupled finite
antiferromagnetic spin-1/2 Heisenberg chain as a channel for transmitting
entanglement. One member of a pair of maximally entangled spins is initially
appended to one end of a chain in its ground state and the dynamical
propagation of this entanglement to the other end is calculated. We show that
compared to the analogous scheme with a ferromagnetic chain in its ground
state, here the entanglement is transmitted faster, with less decay, with a
much higher purity and as a narrow pulse form rising non-analytically from
zero. Here non-zero temperatures and depolarizing environments are both found
to be less destructive in comparison to the ferromagnetic case. The
entanglement is found to propagate through the chain in a peculiar fashion
whereby it hops to skip alternate sites.Comment: 5 pages, 5 figures. Modified version with more explanatio
Quantum communication beyond the localization length in disordered spin chains
We study the effects of localization on quantum state transfer in spin
chains. We show how to use quantum error correction and multiple parallel spin
chains to send a qubit with high fidelity over arbitrary distances; in
particular distances much greater than the localization length of the chain.Comment: 5 pages, 2 figure
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