Hadamard BPSK c-q code

Hadamard BPSK c-q code[1]

Description

Multimode coherent-state c-q code that is a concatenation of a Hadamard code with a BPSK c-q code. Its codewords are \(n\)-mode coherent states whose components \(\pm\alpha\) are arranged according to rows of a Hadamard matrix.

Rate

Using a joint-detection receiver, the code achieves the Holevo capacity of the lossy bosonic channel [1].

Cousins

Hadamard code— The Hadamard BPSK c-q code can be thought of as a concatenation of the Hadamard binary linear code with BPSK for the purposes of transmission of classical information over quantum channels.
Binary PSK (BPSK) code— The Hadamard BPSK c-q code can be thought of as a concatenation of the Hadamard binary linear code with BPSK for the purposes of transmission of classical information over quantum channels.

Member of code lists

Primary Hierarchy

Classical-quantum Domain

Bosonic/analog c-q Kingdom

Bosonic c-q code

Coherent-state c-q code

Parents

Coherent-state c-q code

Concatenated c-q code

The Hadamard BPSK c-q code can be thought of as a concatenation of the Hadamard binary linear code with BPSK for the purposes of transmission of classical information over quantum channels.

Hadamard BPSK c-q code

Children

BPSK c-q code

References

[1]: S. Guha, “Structured Optical Receivers to Attain Superadditive Capacity and the Holevo Limit”, Physical Review Letters 106, (2011) arXiv:1101.1550 DOI

Page edit log

Victor V. Albert (2023-05-31) — most recent

Cite as:

“Hadamard BPSK c-q code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/quantum_hadamard_bpsk

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical_into_quantum/oscillators/coherent_state/psk/quantum_hadamard_bpsk.yml.