Coherent Swap Regret and Channel-Proof Learning
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Quantum Physics arXiv:2606.02655 (quant-ph) [Submitted on 1 Jun 2026] Title:Coherent Swap Regret and Channel-Proof Learning Authors:Sohail Sarkar View a PDF of the paper titled Coherent Swap Regret and Channel-Proof Learning, by Sohail Sarkar View PDF HTML (experimental) Abstract:External regret certifies stability only against replacing one's behavior by a fixed alternative. In a quantum game, this misses a natural physical move: a player can apply a local completely positive trace-preserving (CPTP) map to the state it actually received or prepared. We introduce coherent swap regret as the regret benchmark against all such local CPTP deviations, and give an algorithm achieving $O(\sqrt{dT\log d})$ coherent swap regret via entropic mirror ascent on the CPTP Choi slice with a fixed-point play rule. The main result is a three-level deviation-class landscape. Replacement channels recover ordinary external regret at rate $\Theta(\sqrt{T\log d})$. Unital channels, including unitary deviations and mixtures of unitaries, have zero minimax regret. Deterministic measurement-and-preparation channels already force $\Omega(\sqrt{dT\log d})$ regret in the moderate-horizon regime, and this rate is also sufficient for all CPTP deviations. Thus the hardness comes from non-unital use of the recommendation register, not from quantum coherence alone. As an application, decentralized full-information learning in finite quantum games reaches an $\varepsilon$-approximate separable quantum correlated equilibrium after $T=O(\max_i d_i\log d_i/\varepsilon^2)$ rounds. We identify these equilibria with channel-proofness of mediated quantum recommendation protocols, give an SDP audit for local CPTP exploitability applicable to arbitrary finite-dimensional states, and include a probing-bandit extension with pseudo-regret $O(d^{4/3}T^{2/3}(\log d)^{1/3})$ under Haar-random pure-state probes. Comments: Subjects: Quantum Physics (quant-ph); Computer Science and Game Theory (cs.GT); Machine Learning (cs.LG); Optimization and Control (math.OC) MSC classes: 81P45, 91A26, 91A68, 68Q32, 90C47 ACM classes: F.2.2; G.1.6; I.2.6 Cite as: arXiv:2606.02655 [quant-ph] (or arXiv:2606.02655v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2606.02655 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Sohail Sarkar [view email] [v1] Mon, 1 Jun 2026 05:06:12 UTC (23 KB) Full-text links: Access Paper: View a PDF of the paper titled Coherent Swap Regret and Channel-Proof Learning, by Sohail SarkarView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-06 Change to browse by: cs cs.GT cs.LG math math.OC 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?)