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/0407033 · Open Systems & Information Dynamics

Note on Multiple Additivity of Minimal Renyi Entropy Output of the Werner-Holevo Channels

Robert Alicki, M. Fannes

Published Dec 1, 2004• 35 citations
arXivHTMLPDF

Abstract

We give an elementary self-contained proof that the minimal Renyi entropy output of arbitrary products of channels [Formula: see text] is additive.
DOI
10.1007/s11080-004-6624-4

Related papers

Note on multiple additivity of minimal entropy output of extreme SU(d)-covariant channels

Robert Alicki, M. Fannes

We give an elementary self-contained proof that the minimal entropy output of arbitrary products of channels $\\rho \\mapsto \\frac{1}{d-1}(1-\\rho^T)$ is additive.

•Jul 5, 2004•12 citations

Additivity of the Renyi entropy of order 2 for positive-partial-transpose-inducing channels

B. Dierckx, M. Fannes, Caroline Vandenplas

We prove that the minimal Renyi entropy of order 2 (RE2) output of a positive-partial-transpose (PPT)-inducing channel joint to an arbitrary other channel is equal to the sum of the minimal RE2 output of the individual channels. PPT-inducing channels are channels with a Choi matrix which is bound entangled or separable. The techniques used can be easily recycled to prove additivity for some non-PPT-inducing channels such as the depolarizing and transpose depolarizing channels, though not all known additive channels. We explicitly make the calculations for generalized Werner-Holevo channels as an example of both the scope and limitations of our techniques.

arXiv:0803.0479•Physical Review A•Jun 3, 2008•0 citations

Additivity for some product channels

Christopher King

We show that the Holevo bound, the minimal entropy, and the maximal p-norm are additive (respectively multiplicative) for some product quantum channels. The implications for information capacity of quantum channels are discussed.

Optical Fiber Communication Conference•Jan 1, 2001•0 citations

Additivity properties of a Gaussian channel

Vittorio Giovannetti, Seth Lloyd

The Amosov-Holevo-Werner conjecture implies the additivity of the minimum R\'enyi entropies at the output of a channel. The conjecture is proven true for all R\'enyi entropies of integer order greater than two in a class of Gaussian bosonic channel where the input signal is randomly displaced or where it is coupled linearly to an external environment.

arXiv:quant-ph/0403075•Physical Review A•Jun 7, 2004•62 citations

Non-Additivity of Minimum Output p-$\mathbf{R\acute{e}nyi}$ Entropy

Nengkun Yu, Mingsheng Ying

Hastings disproved additivity conjecture for minimum output entropy by using random unitary channels. In this note, we employ his approach to show that minimum output $p-$Rényi entropy is non-additive for $p\in(0,p_0)\cup(1-p_0,1)$ where $p_0\approx 0.2855$.

arXiv:1006.1733•Jun 9, 2010•0 citations

The minimum Rényi entropy output of a quantum channel is locally additive

Gilad Gour, Todd Kemp

arXiv:1601.00982•Letters in Mathematical Physics•Dec 10, 2016•2 citations
We give an elementary self-contained proof that the minimal entropy output of arbitrary products of channels rhomapstofrac1d−1(1−rhoT)\\rho \\mapsto \\frac{1}{d-1}(1-\\rho^T)rhomapstofrac1d−1(1−rhoT) is additive.
We prove that the minimal Renyi entropy of order 2 (RE2) output of a positive-partial-transpose (PPT)-inducing channel joint to an arbitrary other channel is equal to the sum of the minimal RE2 output of the individual channels. PPT-inducing channels are channels with a Choi matrix which is bound entangled or separable. The techniques used can be easily recycled to prove additivity for some non-PPT-inducing channels such as the depolarizing and transpose depolarizing channels, though not all known additive channels. We explicitly make the calculations for generalized Werner-Holevo channels as an example of both the scope and limitations of our techniques.
Non-Additivity of Minimum Output p-Reˊnyi\mathbf{R\acute{e}nyi}Reˊnyi Entropy
Hastings disproved additivity conjecture for minimum output entropy by using random unitary channels. In this note, we employ his approach to show that minimum output p−p-p−Rényi entropy is non-additive for p∈(0,p0)∪(1−p0,1)p\in(0,p_0)\cup(1-p_0,1)p∈(0,p0​)∪(1−p0​,1) where p0≈0.2855p_0\approx 0.2855p0​≈0.2855.