Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0608010 · Quantum Information Processing

Simplification of Additivity Conjecture in Quantum Information Theory

Motohisa Fukuda

Published Mar 14, 2007• 22 citations
arXivHTMLPDF
DOI
10.1007/s11128-007-0051-8

Related papers

Additivity conjectures in quantum information theory

Motohisa Fukuda

•Jul 10, 2007•0 citations

The additivity conjecture in quantum information theory

Peter W. Shor

In this paper, I discuss the additivity conjecture in quantum information theory.The additivity conjecture was originally a set of at least four conjectures.These conjectures said that certain functions of quantum states and channels were additive under tensor products.While some of these conjectures were previously known to be stronger than others, they have recently all been proved equivalent.This conjecture is a very intriguing mathematical question which the best efforts of a large number of quantum information theorists have not been able to resolve for nearly a decade.It is a mathematically elegant question that is one of the most important open questions in the field of quantum information and computation.This paper then is intended to be both an exposition of the conjecture, its background, and some of the methods that have been used to yield partial results for it, as well as a plea for help in resolving this conjecture.Very recently (summer 2007), substantial progress has been made on this conjecture, in that counterexamples to a set of stronger conjectures have been found.These will be described briefly.

Current Developments in Mathematics•Jan 1, 2005•19 citations

On the additivity hypothesis in quantum information theory

Grigori Gennadievich Amosov, Alexander Semenovich Holevo, Reinhard F. Werner

•Dec 1, 2000•7 citations

On some additivity problems in quantum information theory

Grigori Gennadievich Amosov, Alexander Semenovich Holevo, Reinhard F. Werner

A class of problems in quantum information theory, having an elementary formulation but still resisting solution, concerns the additivity properties of various quantities characterizing quantum channels, notably the "classical capacity", and the "maximal output purity". All known results, including extensive numerical work, are consistent with the conjecture that these quantities are indeed additive (resp. multiplicative) with respect to tensor products of channels. A proof of this conjecture would have important consequences in quantum information theory. In particular, according to this conjecture, the classical capacity or the maximal purity of outputs cannot be increased by using entangled inputs of the channel. In this paper we state the additivity/multiplicativity problems, give some relations between them, and prove some new partial results, which also support the conjecture.

arXiv:math-ph/0003002•Mar 4, 2000•105 citations

On a Sufficient Condition for Additivity in Quantum Information Theory

Nilanjana Datta, Alexander Semenovich Holevo, Yu. M. Suhov

Problems of Information Transmission•Apr 1, 2005•11 citations

Additivity/Multiplicativity Communication Channels

Grigori Gennadievich Amosov, Alexander Semenovich Holevo, Reinhard F. Werner

A class of problems in quantum information theory, having an elementary formulation but still resisting solution, concerns the additivity properties of various quantities characterizing quantum channels, notably the “classical capacity”, and the “maximal output purity”. All known results, including extensive numerical work, are consistent with the conjecture that these quantities are indeed additive (resp. multiplicative) with respect to tensor products of channels. A proof of this conjecture would have important consequences in quantum information theory. In particular, according to this conjecture, the classical capacity or the maximal purity of outputs cannot be increased by using entangled inputs of the channel. In this paper we state the additivity/multiplicativity problems, give some relations between them, and prove some new partial results, which also support the conjecture. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Kluwer Academic Publishers eBooks•Feb 24, 2006•0 citations
In this paper, I discuss the additivity conjecture in quantum information theory.The additivity conjecture was originally a set of at least four conjectures.These conjectures said that certain functions of quantum states and channels were additive under tensor products.While some of these conjectures were previously known to be stronger than others, they have recently all been proved equivalent.This conjecture is a very intriguing mathematical question which the best efforts of a large number of quantum information theorists have not been able to resolve for nearly a decade.It is a mathematically elegant question that is one of the most important open questions in the field of quantum information and computation.This paper then is intended to be both an exposition of the conjecture, its background, and some of the methods that have been used to yield partial results for it, as well as a plea for help in resolving this conjecture.Very recently (summer 2007), substantial progress has been made on this conjecture, in that counterexamples to a set of stronger conjectures have been found.These will be described briefly.
A class of problems in quantum information theory, having an elementary formulation but still resisting solution, concerns the additivity properties of various quantities characterizing quantum channels, notably the "classical capacity", and the "maximal output purity". All known results, including extensive numerical work, are consistent with the conjecture that these quantities are indeed additive (resp. multiplicative) with respect to tensor products of channels. A proof of this conjecture would have important consequences in quantum information theory. In particular, according to this conjecture, the classical capacity or the maximal purity of outputs cannot be increased by using entangled inputs of the channel. In this paper we state the additivity/multiplicativity problems, give some relations between them, and prove some new partial results, which also support the conjecture.
A class of problems in quantum information theory, having an elementary formulation but still resisting solution, concerns the additivity properties of various quantities characterizing quantum channels, notably the “classical capacity”, and the “maximal output purity”. All known results, including extensive numerical work, are consistent with the conjecture that these quantities are indeed additive (resp. multiplicative) with respect to tensor products of channels. A proof of this conjecture would have important consequences in quantum information theory. In particular, according to this conjecture, the classical capacity or the maximal purity of outputs cannot be increased by using entangled inputs of the channel. In this paper we state the additivity/multiplicativity problems, give some relations between them, and prove some new partial results, which also support the conjecture. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.