26,870 research outputs found
Reliability function of general classical-quantum channel
In information theory the reliability function and its bounds, describing the
exponential behavior of the error probability, are the most important
quantitative characteristics of the channel performance. From a general point
of view, these bounds provide certain measures of distinguishability of a given
set of states. In an earlier paper we introduced quantum analogs of the random
coding and the expurgation lower bounds for the case of pure signal states.
Here we discuss the general case, in particular, we prove the previously
conjectured expurgation bound and find the quantum cutoff rate in the case of
arbitrary mixed signal states.Comment: 15 pages, partially reported at the Workshop on Complexity,
Computation and Physics of Information, Cambridge, July 5-23, 1999; to appear
in IEEE Trans. on Information Theory. Several corrections suggested by the
referees are include
Coding Theorems for Quantum Channels
The more than thirty years old issue of the (classical) information capacity
of quantum communication channels was dramatically clarified during the last
years, when a number of direct quantum coding theorems was discovered. The
present paper gives a self contained treatment of the subject, following as
much in parallel as possible with classical information theory and, on the
other side, stressing profound differences of the quantum case. An emphasis is
made on recent results, such as general quantum coding theorems including cases
of infinite (possibly continuous) alphabets and constrained inputs, reliability
function for pure state channels and quantum Gaussian channel. Several still
unsolved problems are briefly outlined.Comment: 41 pages, Latex, eps figure. Extended version of report appeared in
"Tamagawa University Research Review", no. 4, 199
Lov\'asz's Theta Function, R\'enyi's Divergence and the Sphere-Packing Bound
Lov\'asz's bound to the capacity of a graph and the the sphere-packing bound
to the probability of error in channel coding are given a unified presentation
as information radii of the Csisz\'ar type using the R{\'e}nyi divergence in
the classical-quantum setting. This brings together two results in coding
theory that are usually considered as being of a very different nature, one
being a "combinatorial" result and the other being "probabilistic". In the
context of quantum information theory, this difference disappears.Comment: An excerpt from arXiv:1201.5411v3 (with a different notation)
accepted at ISIT 201
Quantum-mechanical communication theory
Optimum signal reception using quantum-mechanical communication theor
Lower Bounds on the Quantum Capacity and Highest Error Exponent of General Memoryless Channels
Tradeoffs between the information rate and fidelity of quantum
error-correcting codes are discussed. Quantum channels to be considered are
those subject to independent errors and modeled as tensor products of copies of
a general completely positive linear map, where the dimension of the underlying
Hilbert space is a prime number. On such a quantum channel, the highest
fidelity of a quantum error-correcting code of length and rate R is proven
to be lower bounded by 1 - \exp [-n E(R) + o(n)] for some function E(R). The
E(R) is positive below some threshold R', which implies R' is a lower bound on
the quantum capacity. The result of this work applies to general discrete
memoryless channels, including channel models derived from a physical law of
time evolution, or from master equations.Comment: 19 pages, 2 figures. Ver.2: Comparisons with the previously known
bounds and examples were added. Except for very noisy channels, this work's
bound is, in general, better than those previously known. Ver.3: Introduction
shortened. Minor change
Constant Compositions in the Sphere Packing Bound for Classical-Quantum Channels
The sphere packing bound, in the form given by Shannon, Gallager and
Berlekamp, was recently extended to classical-quantum channels, and it was
shown that this creates a natural setting for combining probabilistic
approaches with some combinatorial ones such as the Lov\'asz theta function. In
this paper, we extend the study to the case of constant composition codes. We
first extend the sphere packing bound for classical-quantum channels to this
case, and we then show that the obtained result is related to a variation of
the Lov\'asz theta function studied by Marton. We then propose a further
extension to the case of varying channels and codewords with a constant
conditional composition given a particular sequence. This extension is then
applied to auxiliary channels to deduce a bound which can be interpreted as an
extension of the Elias bound.Comment: ISIT 2014. Two issues that were left open in Section IV of the first
version are now solve
- …