Zero-error communication under discrete-time Markovian dynamics

Satvik Singh; Mizanur Rahaman; Nilanjana Datta

doi:10.22331/q-2025-11-14-1910

Zero-error communication under discrete-time Markovian dynamics

Satvik Singh^1,2, Mizanur Rahaman^3,4,5, and Nilanjana Datta²

¹Department of Mathematics, Technical University of Munich
²DAMTP, Centre for Mathematical Sciences, University of Cambridge
³UNIV LYON, INRIA, ENS LYON, UCBL, LIP, F-69342, LYON CEDEX 07, FRANCE
⁴Wallenberg Centre for Quantum Technology, Chalmers University of Technology
⁵Department of Mathematical Sciences, Chalmers University of Technology

Published:	2025-11-14, volume 9, page 1910
Editor:	Philip Taranto
Eprint:	arXiv:2402.18703v3
Doi:	https://doi.org/10.22331/q-2025-11-14-1910
Citation:	Quantum 9, 1910 (2025).

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Abstract

Consider an open quantum system with (discrete-time) Markovian dynamics. Our task is to store information in the system in such a way that it can be retrieved perfectly, even after the system is left to evolve for an arbitrarily long time. We show that this is impossible for classical (resp. quantum) information precisely when the dynamics is mixing (resp. asymptotically entanglement breaking). Furthermore, we provide tight universal upper bounds on the minimum time after which any such dynamics 'scrambles' the encoded information beyond the point of perfect retrieval. On the other hand, for dynamics that are not of this kind, we show that information must be encoded inside the peripheral space associated with the dynamics in order for it to be perfectly recoverable at any time in the future. This allows us to derive explicit formulas for the maximum amount of information that can be protected from noise in terms of the structure of the peripheral space of the dynamics.

► BibTeX data

@article{Singh2025zeroerror,
  doi = {10.22331/q-2025-11-14-1910},
  url = {https://doi.org/10.22331/q-2025-11-14-1910},
  title = {Zero-error communication under discrete-time {M}arkovian dynamics},
  author = {Singh, Satvik and Rahaman, Mizanur and Datta, Nilanjana},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1910},
  month = nov,
  year = {2025}
}

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[3] Omar Fawzi, Mizanur Rahaman, and Mostafa Taheri, "Capacities of quantum Markovian noise for large times", arXiv:2408.00116, (2024).

[4] S. Aravinda, Shilpak Banerjee, and Ranjan Modak, "Ergodic and mixing quantum channels: From two-qubit to many-body quantum systems", Physical Review A 110 4, 042607 (2024).

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