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Bosonic c-q code

Alternative Names: Bosonic c-q modulation format, Bosonic c-q modulation scheme, Bosonic c-q modulation code, Bosonic c-q signaling format.
Root code for the Analog c-q Kingdom

Description

Bosonic code designed for transmission of classical information through non-classical channels. Encodes classical symbols into bosonic quantum states for transmission over a quantum channel and decoding with a quantum-enhanced receiver. This entry includes bosonic c-q modulation formats and is distinct from a classical modulation scheme, which maps classical symbols into classical electromagnetic signals for transmission over classical channels. A bosonic c-q modulation format instead treats the transmitted signals as quantum states and allows the receiver to use quantum measurements.

Rate

The Holevo capacity has been calculated for various bosonic quantum channels [1–3] such as the pure-loss bosonic channel [4] or quantum AWGN [5]. The energy-constrained capacity of the noiseless bosonic c-q channel is finite due to quantum effects [6,7], while the Shannon capacity can be infinite. Gordon was the first to calculate such capacities (in a published work) for a specific case [8–10], and a related discussion is given by Forney [11]. The most information-efficient format of a transmitted message is indistinguishable from black-body radiation [12].

Cousins

  • Bosonic code— Bosonic c-q codes are bosonic codes designed to transmit classical information.
  • Modulation scheme— Classical modulation schemes transmit classical signals over classical channels, while bosonic c-q modulation formats transmit quantum states over quantum channels and can use quantum-enhanced receivers.
  • Analog code— Any analog code can be embedded into a bosonic Hilbert space, and thus passed through a bosonic channel, by associating the reals with the configuration space of position states of bosonic modes.
  • Entanglement-assisted (EA) c-q code— Bosonic EA c-q schemes use pre-shared continuous-variable entanglement to assist bosonic c-q communication, including structured transceivers for lossy thermal-noise channels [13,14].

Member of code lists

Primary Hierarchy

Classical-quantum Domain
Analog c-q Kingdom
Parents
Classical-quantum (c-q) code
Bosonic c-q code
Children
Coherent-state c-q modulation format
Fock-state OOK c-q modulation format
Niset-Andersen-Cerf code
Squeezed-coherent BPSK c-q modulation format

References

[1]
J. H. Shapiro, “The Quantum Theory of Optical Communications”, IEEE Journal of Selected Topics in Quantum Electronics 15, 1547 (2009) DOI
[2]
K. Banaszek, L. Kunz, M. Jachura, and M. Jarzyna, “Quantum Limits in Optical Communications”, Journal of Lightwave Technology 38, 2741 (2020) arXiv:2002.05766 DOI
[3]
A. S. Holevo, “Quantum Systems, Channels, Information”, (2019) DOI
[4]
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”, Physical Review Letters 92, (2004) arXiv:quant-ph/0308012 DOI
[5]
V. Giovannetti, R. García-Patrón, N. J. Cerf, and A. S. Holevo, “Ultimate classical communication rates of quantum optical channels”, Nature Photonics 8, 796 (2014) arXiv:1312.6225 DOI
[6]
H. P. Yuen and M. Ozawa, “Ultimate information carrying limit of quantum systems”, Physical Review Letters 70, 363 (1993) DOI
[7]
C. M. Caves and P. D. Drummond, “Quantum limits on bosonic communication rates”, Reviews of Modern Physics 66, 481 (1994) DOI
[8]
J. P. Gordon, in Advances in Quantum Electronics edited by J. R. Singer (Columbia University, New York, 1961), p. 509
[9]
J. Gordon, “Quantum Effects in Communications Systems”, Proceedings of the IRE 50, 1898 (1962) DOI
[10]
J. P. Gordon, in Quantum Electronics and Coherent Light, Proceedings of the International School of Physics “Enrico Fermi”, Course XXXI, edited by PA. Miles (Academic, New York, 1964), p. 156
[11]
G. D. Forney, Jr., S.M. thesis, Massachusetts Institute of Technology, 1963 (unpublished)
[12]
M. Lachmann, M. E. J. Newman, and C. Moore, “The physical limits of communication or Why any sufficiently advanced technology is indistinguishable from noise”, American Journal of Physics 72, 1290 (2004) arXiv:cond-mat/9907500 DOI
[13]
S. Guha, Q. Zhuang, and B. A. Bash, “Infinite-fold enhancement in communications capacity using pre-shared entanglement”, 2020 IEEE International Symposium on Information Theory (ISIT) 1835 (2020) arXiv:2001.03934 DOI
[14]
A. Cox, Q. Zhuang, C. N. Gagatsos, B. Bash, and S. Guha, “Transceiver Designs Approaching the Entanglement-Assisted Communication Capacity”, Physical Review Applied 19, (2023) arXiv:2208.07979 DOI
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Zoo Code ID: bosonic_classical_into_quantum

Cite as:
“Bosonic c-q code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/bosonic_classical_into_quantum, arXiv:2606.11484
BibTeX:
@incollection{eczoo_bosonic_classical_into_quantum,
title={Bosonic c-q code},
booktitle={The Error Correction Zoo},
year={2026},
editor={Albert, Victor V. and Faist, Philippe},
eprint={2606.11484},
doi={10.48550/arXiv.2606.11484},
url={https://errorcorrectionzoo.org/c/bosonic_classical_into_quantum}
}
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Permanent link:
https://errorcorrectionzoo.org/c/bosonic_classical_into_quantum

Cite as:

“Bosonic c-q code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2026. https://errorcorrectionzoo.org/c/bosonic_classical_into_quantum, arXiv:2606.11484

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical_into_quantum/oscillators/bosonic_classical_into_quantum.yml.