PPM c-q code[1]
Description
A \(q\)-PPM c-q code is a coherent-state c-q code whose \(j\)th codeword corresponds to a tensor-product state of zero-amplitude coherent states at all modes except mode \(j\). For example, a 3-PPM encoding corresponds to the three-mode states \(|\alpha\rangle|0\rangle|0\rangle\), \(|0\rangle|\alpha\rangle|0\rangle\), and \(|0\rangle|0\rangle|\alpha\rangle\) for some complex \(\alpha\). The dual of a PPM code is obtained by the exchange \(0\leftrightarrow\alpha\).
Protection
The error probability under an optimal quantum detector is worked out in [2; Sec. IV.2].
Decoding
Conditional pulse nulling (CPN) receiver [3].
Realizations
Conditional pulse nulling (CPN) receiver [1].
Parent
Cousins
- Pulse-position modulation (PPM) code
- One-hot code — The PPM c-q code is an continuous analogue of the one-hot code designed for transmission through quantum channels.
References
- [1]
- J. Chen et al., “Optical codeword demodulation with error rates below the standard quantum limit using a conditional nulling receiver”, Nature Photonics 6, 374 (2012) arXiv:1111.4017 DOI
- [2]
- Carl W. Helstrom. Quantum Detection and Estimation Theory. Elsevier, 1976.
- [3]
- S. J. Dolinar, Jr., “A near-optimum receiver structure for the detection of M-ary optical PPM signals”, The Telecommunications and Data Acquisition Progress Report 42 72: December 1982; NASA: Pasadena, CA, (1983)
Page edit log
- Victor V. Albert (2022-12-04) — most recent
Cite as:
“PPM c-q code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022. https://errorcorrectionzoo.org/c/quantum_ppm