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  • Open Access

No practical quantum broadcasting: General framework

Yunlong Xiao1,2,*, Xiangjing Liu3,4,5,6, and Zhenhuan Liu7,†

  • 1Quantum Innovation Centre (Q.InC), Agency for Science Technology and Research (A*STAR), 2 Fusionopolis Way, Innovis #08-03, Singapore 138634, Republic of Singapore
  • 2Institute of High Performance Computing (IHPC), Agency for Science, Technology and Research (A*STAR), 1 Fusionopolis Way, #16-16 Connexis, Singapore 138632, Republic of Singapore
  • 3Nanyang Quantum Hub, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371, Republic of Singapore
  • 4CNRS@CREATE, 1 Create Way, 08-01 Create Tower, Singapore 138602, Republic of Singapore
  • 5MajuLab, CNRS-UCA-SU-NUS-NTU International Joint Research Laboratory, Republic of Singapore
  • 6Centre for Quantum Technologies, National University of Singapore, Singapore 117543, Republic of Singapore
  • 7Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China

  • *Contact author: mathxiao123@gmail.com
  • †Contact author: liu-zh20@mails.tsinghua.edu.cn
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Phys. Rev. Research 7, 033194 – Published 26 August, 2025

DOI: https://doi.org/10.1103/8g6j-w7ld

Abstract

We introduce a comprehensive framework for no practical broadcasting, demonstrating that no linear map can simultaneously meet the conditions of sample efficiency, unitary covariance, permutation invariance, and classical consistency. This work establishes a rigorous theoretical foundation and provides an in-depth analysis of the employed techniques. In particular, we apply Schur-Weyl duality to provide a simplified alternative proof for the uniqueness of linear maps, referred to as the canonical virtual broadcasting map, that satisfy unitary covariance, permutation invariance, and classical consistency. The sample complexity of this canonical map is determined through semidefinite programming. Expanding beyond the 1-to-2 case, we derive the canonical form for 1-to-N virtual broadcasting, analyze the sample complexity involved in its realization, and explore its connections with temporal quantum states and pseudodensity operators.

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See Also

No Practical Quantum Broadcasting: Even Virtually

Yunlong Xiao, Xiangjing Liu, and Zhenhuan Liu
Phys. Rev. Lett. 135, 090202 (2025)

Article Text

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Phys. Rev. Research 7, 033194– Published 26 August, 2025
  • Received 28 March 2025
  • Accepted 22 July 2025
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