579 research outputs found
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
Quantum Shannon Theory
This is the 10th and final chapter of my book on Quantum Information, based
on the course I have been teaching at Caltech since 1997. An early version of
this chapter (originally Chapter 5) has been available on the course website
since 1998, but this version is substantially revised and expanded. The level
of detail is uneven, as I've aimed to provide a gentle introduction, but I've
also tried to avoid statements that are incorrect or obscure. Generally
speaking, I chose to include topics that are both useful to know and relatively
easy to explain; I had to leave out a lot of good stuff, but on the other hand
the chapter is already quite long. This is a working draft of Chapter 10, which
I will continue to update. See the URL on the title page for further updates
and drafts of other chapters, and please send me an email if you notice errors.
Eventually, the complete book will be published by Cambridge University Press
Enhanced communication with the assistance of indefinite causal order
In quantum Shannon theory, the way information is encoded and decoded takes
advantage of the laws of quantum mechanics, while the way communication
channels are interlinked is assumed to be classical. In this Letter we relax
the assumption that quantum channels are combined classically, showing that a
quantum communication network where quantum channels are combined in a
superposition of different orders can achieve tasks that are impossible in
conventional quantum Shannon theory. In particular, we show that two identical
copies of a completely depolarizing channel become able to transmit information
when they are combined in a quantum superposition of two alternative orders.
This finding runs counter to the intuition that if two communication channels
are identical, using them in different orders should not make any difference.
The failure of such intuition stems from the fact that a single noisy channel
can be a random mixture of elementary, non-commuting processes, whose order (or
lack thereof) can affect the ability to transmit information
From Classical to Quantum Shannon Theory
The aim of this book is to develop "from the ground up" many of the major,
exciting, pre- and post-millenium developments in the general area of study
known as quantum Shannon theory. As such, we spend a significant amount of time
on quantum mechanics for quantum information theory (Part II), we give a
careful study of the important unit protocols of teleportation, super-dense
coding, and entanglement distribution (Part III), and we develop many of the
tools necessary for understanding information transmission or compression (Part
IV). Parts V and VI are the culmination of this book, where all of the tools
developed come into play for understanding many of the important results in
quantum Shannon theory.Comment: v8: 774 pages, 301 exercises, 81 figures, several corrections; this
draft, pre-publication copy is available under a Creative Commons
Attribution-NonCommercial-ShareAlike license (see
http://creativecommons.org/licenses/by-nc-sa/3.0/), "Quantum Information
Theory, Second Edition" is available for purchase from Cambridge University
Pres
The quantum dynamic capacity formula of a quantum channel
The dynamic capacity theorem characterizes the reliable communication rates
of a quantum channel when combined with the noiseless resources of classical
communication, quantum communication, and entanglement. In prior work, we
proved the converse part of this theorem by making contact with many previous
results in the quantum Shannon theory literature. In this work, we prove the
theorem with an "ab initio" approach, using only the most basic tools in the
quantum information theorist's toolkit: the Alicki-Fannes' inequality, the
chain rule for quantum mutual information, elementary properties of quantum
entropy, and the quantum data processing inequality. The result is a simplified
proof of the theorem that should be more accessible to those unfamiliar with
the quantum Shannon theory literature. We also demonstrate that the "quantum
dynamic capacity formula" characterizes the Pareto optimal trade-off surface
for the full dynamic capacity region. Additivity of this formula simplifies the
computation of the trade-off surface, and we prove that its additivity holds
for the quantum Hadamard channels and the quantum erasure channel. We then
determine exact expressions for and plot the dynamic capacity region of the
quantum dephasing channel, an example from the Hadamard class, and the quantum
erasure channel.Comment: 24 pages, 3 figures; v2 has improved structure and minor corrections;
v3 has correction regarding the optimizatio
Communicating via ignorance: Increasing communication capacity via superposition of order
Classically, no information can be transmitted through a depolarising, that
is a completely noisy, channel. We show that by combining a depolarising
channel with another channel in an indefinite causal order---that is, when
there is superposition of the order that these two channels were applied---it
becomes possible to transmit significant information. We consider two limiting
cases. When both channels are fully-depolarising, the ideal limit is
communication of 0.049 bits; experimentally we achieve
bits. When one channel is fully-depolarising,
and the other is a known unitary, the ideal limit is communication of 1 bit. We
experimentally achieve 0.640.02 bits. Our results offer intriguing
possibilities for future communication strategies beyond conventional quantum
Shannon theory
Exact Cost of Redistributing Multipartite Quantum States
How correlated are two quantum systems from the perspective of a third? We answer this by providing an optimal “quantum state redistribution” protocol for multipartite product sources. Specifically, given an arbitrary quantum state of three systems, where Alice holds two and Bob holds one, we identify the cost, in terms of quantum communication and entanglement, for Alice to give one of her parts to Bob. The communication cost gives the first known operational interpretation to quantum conditional mutual information. The optimal procedure is self-dual under time reversal and is perfectly composable. This generalizes known protocols such as the state merging and fully quantum Slepian-Wolf protocols, from which almost every known protocol in quantum Shannon theory can be derived
- …