Approximate virtual quantum broadcasting

Quantum Physics [Submitted on 19 Mar 2026] Approximate virtual quantum broadcasting Matthew Simon Tan, Davit Aghamalyan, Varun Narasimhachar The no-broadcasting theorem, a fundamental limitation on the communication of quantum information, holds that a physical process cannot broadcast copies of an unknown quantum state to two or more receivers. Recent work has explored ways of circumventing this limitation using "virtual" implementations of non-physical processes using measurement and data-processing on statistical samples of the unknown input. However, the statistical fluctuations of this data degrades the virtual copies so much that the protocol effectively depletes, rather than proliferate, the sample size -- thereby rendering it worse than the "naive" approach of splitting the given sample and sending a subsample to each receiver. In this work, we circumvent this flaw by allowing a small amount of systematic bias in the broadcast data, resulting in approximate virtual copies. We provide efficient semidefinite programs (SDP's) to determine the minimum sample size required to keep the approximation error below a desired threshold and vice versa. For reasonably small error values, we find approximate virtual broadcasting to be viable with sample sizes smaller than naive sample-splitting would demand. Along the way, we prove several symmetry-based simplifications to the problem, allowing optimal approximate broadcasting to be characterized in terms of the simple class of depolarizing channels. Comments: 9+6 pages. PDF-only upload due to arXiv technical issues; source will be uploaded in subsequent revision Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.19476 [quant-ph]   (or arXiv:2603.19476v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.19476 Focus to learn more Submission history From: Varun Narasimhachar [view email] [v1] Thu, 19 Mar 2026 21:17:16 UTC (1,369 KB) Access Paper: view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation 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 Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)