22 research outputs found
On converse bounds for classical communication over quantum channels
We explore several new converse bounds for classical communication over
quantum channels in both the one-shot and asymptotic regimes. First, we show
that the Matthews-Wehner meta-converse bound for entanglement-assisted
classical communication can be achieved by activated, no-signalling assisted
codes, suitably generalizing a result for classical channels. Second, we derive
a new efficiently computable meta-converse on the amount of classical
information unassisted codes can transmit over a single use of a quantum
channel. As applications, we provide a finite resource analysis of classical
communication over quantum erasure channels, including the second-order and
moderate deviation asymptotics. Third, we explore the asymptotic analogue of
our new meta-converse, the -information of the channel. We show that
its regularization is an upper bound on the classical capacity, which is
generally tighter than the entanglement-assisted capacity and other known
efficiently computable strong converse bounds. For covariant channels we show
that the -information is a strong converse bound.Comment: v3: published version; v2: 18 pages, presentation and results
improve
Lossless Source Coding in the Point-to-Point, Multiple Access, and Random Access Scenarios
This paper treats point-to-point, multiple access and random access lossless
source coding in the finite-blocklength regime. A random coding technique is
developed, and its power in analyzing the third-order coding performance is
demonstrated in all three scenarios. Via a connection to composite hypothesis
testing, a new converse that tightens previously known converses for
Slepian-Wolf source coding is established. Asymptotic results include a
third-order characterization of the Slepian-Wolf rate region and a proof
showing that for dependent sources, the independent encoders used by
Slepian-Wolf codes can achieve the same third-order-optimal performance as a
single joint encoder. The concept of random access source coding, which
generalizes the multiple access scenario to allow for a subset of participating
encoders that is unknown a priori to both the encoders and the decoder, is
introduced. Contributions include a new definition of the probabilistic model
for a random access source, a general random access source coding scheme that
employs a rateless code with sporadic feedback, and an analysis demonstrating
via a random coding argument that there exists a deterministic code of the
proposed structure that simultaneously achieves the third-order-optimal
performance of Slepian-Wolf codes for all possible subsets of encoders.Comment: 42 pages, 10 figures. Part of this work was presented at ISIT'1
A Resource Framework for Quantum Shannon Theory
Quantum Shannon theory is loosely defined as a collection of coding theorems,
such as classical and quantum source compression, noisy channel coding
theorems, entanglement distillation, etc., which characterize asymptotic
properties of quantum and classical channels and states. In this paper we
advocate a unified approach to an important class of problems in quantum
Shannon theory, consisting of those that are bipartite, unidirectional and
memoryless.
We formalize two principles that have long been tacitly understood. First, we
describe how the Church of the larger Hilbert space allows us to move flexibly
between states, channels, ensembles and their purifications. Second, we
introduce finite and asymptotic (quantum) information processing resources as
the basic objects of quantum Shannon theory and recast the protocols used in
direct coding theorems as inequalities between resources. We develop the rules
of a resource calculus which allows us to manipulate and combine resource
inequalities. This framework simplifies many coding theorem proofs and provides
structural insights into the logical dependencies among coding theorems.
We review the above-mentioned basic coding results and show how a subset of
them can be unified into a family of related resource inequalities. Finally, we
use this family to find optimal trade-off curves for all protocols involving
one noisy quantum resource and two noiseless ones.Comment: 60 page