6 research outputs found
Extensions of the quantum Fano inequality
Quantum Fano inequality (QFI) in quantum information theory provides an upper
bound to the entropy exchange by a function of the entanglement fidelity. We
give various Fano-like upper bounds to the entropy exchange and QFI is a
special case of these bounds. These bounds also give an alternate derivation of
the QFI.Comment: 8 pages, 2 figures, took care of referees' comments, to appear in
Physical Review
On the strong converses for the quantum channel capacity theorems
A unified approach to prove the converses for the quantum channel capacity
theorems is presented. These converses include the strong converse theorems for
classical or quantum information transfer with error exponents and novel
explicit upper bounds on the fidelity measures reminiscent of the Wolfowitz
strong converse for the classical channel capacity theorems. We provide a new
proof for the error exponents for the classical information transfer. A long
standing problem in quantum information theory has been to find out the strong
converse for the channel capacity theorem when quantum information is sent
across the channel. We give the quantum error exponent thereby giving a
one-shot exponential upper bound on the fidelity. We then apply our results to
show that the strong converse holds for the quantum information transfer across
an erasure channel for maximally entangled channel inputs.Comment: Added the strong converse for the erasure channel for maximally
entangled inputs and corrected minor typo
The Sphere Packing Bound For Memoryless Channels
Sphere packing bounds (SPBs) ---with prefactors that are polynomial in the
block length--- are derived for codes on two families of memoryless channels
using Augustin's method: (possibly non-stationary) memoryless channels with
(possibly multiple) additive cost constraints and stationary memoryless
channels with convex constraints on the composition (i.e. empirical
distribution, type) of the input codewords. A variant of Gallager's bound is
derived in order to show that these sphere packing bounds are tight in terms of
the exponential decay rate of the error probability with the block length under
mild hypotheses.Comment: 29 page