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Probabilistic pulse-position modulation for classical communication on quantum channels

Farzad Kianvash* and Matteo Rosati

  • Dipartimento di Ingegneria Civile, Informatica e delle Tecnologie Aeronautiche, Università Roma Tre, Via Vito Volterra 62, I-00146 Rome, Italy

  • *Contact author: farzad.kianvash@uniroma3.it
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Phys. Rev. A 112, 032624 – Published 25 September, 2025

DOI: https://doi.org/10.1103/jx7h-nz4c

Abstract

Classical communication over lossy quantum channels is an essential topic in quantum information theory, with practical implications for optical-fiber and free-space communications. Multiphase Hadamard codes, based on coherent-state binary phase-shift keying (BPSK) modulation and decoded using vacuum-or-pulse (VP) detectors, offer a promising approach for achieving high communication rates while relying only on linear optics and single-photon detectors (SPDs). However, their performance does not reach the ultimate Holevo limit. In this work, we propose a generalization of Hadamard codes that distributes the signal across multiple modes with optimized probabilities, rather than concentrating it in a single mode, dubbed probabilistic pulse-position modulation (PPPM). We derive an achievable communication rate, demonstrating that our PPPM can outperform traditional Hadamard codes in certain intermediate energy regimes.

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References (35)

  1. K. Banaszek, L. Kunz, M. Jachura, and M. Jarzyna, Quantum limits in optical communications, J. Lightwave Technol. 38, 2741 (2020).
  2. A. S. Holevo, Quantum Systems, Channels, Information (De Gruyter, Berlin, 2012).
  3. A. Serafini, Quantum Continuous Variables: A Primer of Theoretical Methods (CRC Press, Boca Raton, FL, 2023).
  4. P. Hausladen and W. K. Wootters, A ‘pretty good’ measurement for distinguishing quantum states, J. Mod. Opt. 41, 2385 (1994).
  5. B. Schumacher and M. D. Westmoreland, Sending classical information via noisy quantum channels, Phys. Rev. A 56, 131 (1997).
  6. S. Lloyd, V. Giovannetti, and L. Maccone, Sequential projective measurements for channel decoding, Phys. Rev. Lett. 106, 250501 (2011).
  7. V. Giovannetti, S. Lloyd, and L. Maccone, Achieving the Holevo bound via sequential measurements, Phys. Rev. A 85, 012302 (2012).
  8. P. Sen, Achieving the Han-Kobayashi inner bound for the quantum interference channel, in Proceedings of the 2012 IEEE International Symposium on Information Theory Proceedings (IEEE, New York, 2012), pp. 736–740.
  9. M. M. Wilde, O. Landon-Cardinal, and P. Hayden, Towards efficient decoding of classical-quantum polar codes, Proceedings of the 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC) (Schloss Dagstuhl, Leibniz-Zentrum für Informatik, 2013), pp. 157–177.
  10. M. M. Wilde and S. Guha, Polar codes for classical-quantum channels, IEEE Trans. Inf. Theory 59, 1175 (2012).
  11. C. Cui, J. Postlewaite, B. N. Saif, L. Fan, and S. Guha, Superadditive communications with the Green machine as a practical demonstration of nonlocality without entanglement, Nat. Commun. 16, 3760 (2025).
  12. M. Rosati and G. Cincotti, Optical communications at the quantum limit, in Proceedings of the 2024 24th International Conference on Transparent Optical Networks (IEEE, New York, 2024), p. 1-S-4.
  13. M. Rosati and G. Cincotti, A Fourier machine for quantum optical communications, J. Light. Technol. 43, 3770 (2025).
  14. V. Giovannetti, S. Guha, S. Lloyd, L. Maccone, J. H. Shapiro, and H. P. Yuen, Classical capacity of the lossy bosonic channel: The exact solution, Phys. Rev. Lett. 92, 027902 (2004).
  15. A. Klimek, M. Jachura, W. Wasilewski, and K. Banaszek, Quantum memory receiver for superadditive communication using binary coherent states, J. Mod. Opt. 63, 2074 (2016).
  16. M. Jarzyna, V. Lipińska, A. Klimek, K. Banaszek, and M. G. A. Paris, Phase noise in collective binary phase shift keying with Hadamard words, Opt. Express 24, 1693 (2016).
  17. M. Rosati, Performance of coherent frequency-shift keying for classical communication on quantum channels, in Proceedings of the 2021 IEEE International Symposium on Information Theory (IEEE, New York, 2021), pp. 902–905.
  18. M. Rosati, Multi-pulse Fourier codes for bit transmission at the quantum limit, New J. Phys. 27, 013010 (2025).
  19. M. Rosati, A. Mari, and V. Giovannetti, Multiphase Hadamard receivers for classical communication on lossy bosonic channels, Phys. Rev. A 94, 062325 (2016).
  20. N. Rengaswamy, K. P. Seshadreesan, S. Guha, and H. D. Pfister, Belief propagation with quantum messages for quantum-enhanced classical communications, npj Quantum Inf. 7, 97 (2021).
  21. S. Guha, Z. Dutton, and J. H. Shapiro, On quantum limit of optical communications: Concatenated codes and joint-detection receivers, 2011 IEEE International Symposium on Information Theory Proceedings (IEEE, Piscataway, NJ, 2011).
  22. S. Guha, Structured optical receivers to attain superadditive capacity and the Holevo limit, Phys. Rev. Lett. 106, 240502 (2011).
  23. C. Guo, S. K. Dacha, R. J. Essiambre, A. Ashikhmin, A. Blanco-Redondo, F. R. Kschischang, K. Banaszek, M. Weiner, R. Kopf, I. Crawley, M. H. Idjadi, A. A. Sayem, J. Zhao, J. D. Sandoz, N. Fontaine, N. Menkart, R. Ryf, J. Cloonan, M. Vasilyev, T. E. Murphy, and E. C. Burrows, Record photon information efficiency with optical clock transmission and recovery of 12.5 bits/photon over an optical channel with 77 dB loss, 2023 IEEE Photonics Conference (IPC) (IEEE, Piscataway, NJ, 2023).
  24. M. Rosati and V. Giovannetti, Achieving the Holevo bound via a bisection decoding protocol, J. Math. Phys. 57, 062204 (2016).
  25. S. J. Dolinar, Jr., An optimum receiver for the binary coherent state quantum channel, Q. Prog. Rep. (Research Lab. Electron. 111, 115 (1973).
  26. R. L. Cook, P. J. Martin, J. M. Geremia, B. A. Chase, and J. M. Geremia, Optical coherent state discrimination using a closed-loop quantum measurement, Nature (London) 446, 774 (2007).
  27. F. E. Becerra, J. Fan, G. Baumgartner, J. Goldhar, J. T. Kosloski, and A. Migdall, Experimental demonstration of a receiver beating the standard quantum limit for multiple nonorthogonal state discrimination, Nat. Photon. 7, 147 (2013).
  28. A. S. Holevo, Quantum-probabilistic investigation of the statistics of readings, using a “Dolinar device”, Izv. Vuz. Matematika 26, 3 (1982) [Sov. Math. 26, 1 (1982)].
  29. M. Takeoka, M. Sasaki, P. Van Loock, and N. Lütkenhaus, Implementation of projective measurements with linear optics and continuous photon counting, Phys. Rev. A 71, 022318 (2005).
  30. A. Assalini, N. Dalla Pozza, and G. Pierobon, Revisiting the Dolinar receiver through multiple-copy state discrimination theory, Phys. Rev. A 84, 022342 (2011).
  31. D. Sych and G. Leuchs, Practical receiver for optimal discrimination of binary coherent signals, Phys. Rev. Lett. 117, 200501 (2016).
  32. J. M. Geremia, Distinguishing between optical coherent states with imperfect detection, Phys. Rev. A 70, 062303 (2004).
  33. Quantum Detection and Estimation Theory, Mathematics in Science and Engineering (Academic Press, New York, 1976).
  34. M. Rosati and A. Solana, Joint-detection learning for optical communication at the quantum limit, Opt. Quantum 2, 390 (2024).
  35. The data of Figs. 2, 3, 4: https://doi.org/10.6084/m9.figshare.29337764.v1.

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Phys. Rev. A 112, 032624– Published 25 September, 2025
  • Received 3 March 2025
  • Accepted 23 May 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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