Additivity Results for the R\'enyi-2 Entanglement of Purification
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Quantum Physics arXiv:2605.15439 (quant-ph) [Submitted on 14 May 2026] Title:Additivity Results for the Rényi-2 Entanglement of Purification Authors:Shokoufe Faraji, Zahra Baghali Khanian View a PDF of the paper titled Additivity Results for the R\'enyi-2 Entanglement of Purification, by Shokoufe Faraji and Zahra Baghali Khanian View PDF HTML (experimental) Abstract:We reformulate the Rényi entanglement of purification as a constrained minimum output Rényi entropy problem. Equivalently, for $p>1$, this formulation can be expressed in terms of a constrained maximal output Schatten $p$-norm. More precisely, for a completely positive map $\Omega:L(B')\to L(A)$, we consider the quantity $\upsilon_p(\Omega)$ defined by optimizing $\|(\Omega\otimes \mathrm{id}_E)(\sigma^{B'E})\|_p$ over all bipartite states $\sigma^{B'E}$ whose $B'$-marginal is maximally mixed. We focus on the case $p=2$. First, we compute $\upsilon_2$ for the transpose-depolarizing channel and prove that it is multiplicative under tensor powers. We then establish a general multiplicativity criterion: whenever a completely positive map $N:L(B')\to L(A)$ satisfies $N^{\dagger} \mathbin{\circ} N=a\,\mathrm{id}_A+b\,\mathrm{Tr}[\cdot]\,I_d$ for some constants $a,b\ge 0$, where $N^{\dagger}$ denotes the Hilbert-Schmidt adjoint of $N$, the quantity $\upsilon_2(N)$ is multiplicative under tensor powers. Examples of channels satisfying this criterion include the transpose-depolarizing channel, the depolarizing channel, and their respective complementary channels. Furthermore, we show that, for every completely positive map $\Omega$, multiplicativity of $\upsilon_p(\Omega)$ implies multiplicativity for its complementary map. This yields the corresponding additivity statements for the associated Rényi-2 entanglement of purification. Subjects: Quantum Physics (quant-ph); Information Theory (cs.IT) Cite as: arXiv:2605.15439 [quant-ph] (or arXiv:2605.15439v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.15439 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Zahra Baghali Khanian [view email] [v1] Thu, 14 May 2026 21:41:31 UTC (35 KB) Full-text links: Access Paper: View a PDF of the paper titled Additivity Results for the R\'enyi-2 Entanglement of Purification, by Shokoufe Faraji and Zahra Baghali KhanianView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-05 Change to browse by: cs cs.IT math math.IT References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)