Coherent-state constellation code 

Description

Qudit-into-oscillator code whose codewords can succinctly be expressed as superpositions of a countable set of coherent states that is called a constellation. Some useful constellations form a group (see gkp, cat or \(2T\)-qutrit codes) while others make up a Gaussian quadrature rule [1,2].

Rate

Coherent-state constellation codes consisting of points from a Gaussian quadrature rule can be concatenated with quantum polar codes to achieve the Gaussian coherent information of the thermal noise channel [1,2].

Parent

Children

Cousins

  • Quantum polar code — Coherent-state constellation codes consisting of points from a Gaussian quadrature rule can be concatenated with quantum polar codes to achieve the Gaussian coherent information of the thermal noise channel [1,2].
  • Concatenated bosonic code — Coherent-state constellation codes consisting of points from a Gaussian quadrature rule can be concatenated with quantum polar codes to achieve the Gaussian coherent information of the thermal noise channel [1,2].
  • Modulation scheme — Coherent-state constellation codes are quantum versions of modulation schemes in that their codewords are superpositions of points in a constellation. Additionally, analog codes that achieve AGWN capacity [5] can be used to develop capacity-achieving concatenations of coherent-state constellation codes with quantum polar codes [1,2].
  • Coherent-state c-q code — Coherent-state c-q codes encode classical alphabets into constellations of coherent states, while coherent-state constellation codes encode quantum information into superpositions of coherent states.

References

[1]
F. Lacerda, J. M. Renes, and V. B. Scholz, “Coherent-state constellations and polar codes for thermal Gaussian channels”, Physical Review A 95, (2017) arXiv:1603.05970 DOI
[2]
F. Lacerda, J. M. Renes, and V. B. Scholz, “Coherent state constellations for Bosonic Gaussian channels”, 2016 IEEE International Symposium on Information Theory (ISIT) (2016) DOI
[3]
D. Gottesman, A. Kitaev, and J. Preskill, “Encoding a qubit in an oscillator”, Physical Review A 64, (2001) arXiv:quant-ph/0008040 DOI
[4]
V. V. Albert et al., “Performance and structure of single-mode bosonic codes”, Physical Review A 97, (2018) arXiv:1708.05010 DOI
[5]
Y. Wu and S. Verdu, “The impact of constellation cardinality on Gaussian channel capacity”, 2010 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton) (2010) DOI
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Zoo Code ID: coherent_constellation

Cite as:
“Coherent-state constellation code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/coherent_constellation
BibTeX:
@incollection{eczoo_coherent_constellation, title={Coherent-state constellation code}, booktitle={The Error Correction Zoo}, year={2023}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/coherent_constellation} }
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“Coherent-state constellation code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/coherent_constellation

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/quantum/oscillators/coherent_state/coherent_constellation.yml.