6 research outputs found
Expurgation Exponent of Leaked Information in Privacy Amplification for Binary Sources
We investigate the privacy amplification problem in which Eve can observe the
uniform binary source through a binary erasure channel (BEC) or a binary
symmetric channel (BSC). For this problem, we derive the so-called expurgation
exponent of the information leaked to Eve. The exponent is derived by relating
the leaked information to the error probability of the linear code that is
generated by the linear hash function used in the privacy amplification, which
is also interesting in its own right. The derived exponent is larger than
state-of-the-art exponent recently derived by Hayashi at low rate.Comment: 5 pages, 7 figures, to be presented at IEEE Information Theory
Workshop (ITW) 201
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