Coherent FSK (CFSK) c-q code[1,2] 


Coherent-state c-q code encoding into coherent states that are frequency-shifted with certain initial relative phase.

Codewords are coherent states \(|\alpha_m\rangle\), where \begin{align} \alpha_m = \alpha e^{i(\omega_0+[m-1]\Delta\omega)t+i(m-1)\Delta\theta} \tag*{(1)}\end{align} for common frequency \(\omega_0\), frequency shift \(\Delta\omega < 2\pi/T\), total time \(T\), and phase shift \(\Delta\theta\).


The square-root measurement is not optimal for CFSK c-q codes, unlike for PSK c-q codes [3].


Bondurant receiver [4].Cyclic receiver [5].Time-resolving receiver [1,2,6].Bayesian inference [1].


Time-resolving quantum receiver [6].Bondurant receiver [5].Bayesian inference [2].



  • PSK c-q code — The CFSK c-q code reduces to the \(q\)-ary PSK c-q code when \(\Delta\omega = 0\) and \(\Delta\theta = 2\pi/q\).



I. A. Burenkov, O. V. Tikhonova, and S. V. Polyakov, “Quantum receiver for large alphabet communication”, Optica 5, 227 (2018) arXiv:1802.08287 DOI
I. A. Burenkov et al., “Time-Resolving Quantum Measurement Enables Energy-Efficient, Large-Alphabet Communication”, PRX Quantum 1, (2020) DOI
M. Rosati, “Performance of Coherent Frequency-Shift Keying for Classical Communication on Quantum Channels”, 2021 IEEE International Symposium on Information Theory (ISIT) (2021) arXiv:2203.09822 DOI
R. S. Bondurant, “Near-quantum optimum receivers for the phase-quadrature coherent-state channel”, Optics Letters 18, 1896 (1993) DOI
M. V. Jabir et al., “Experimental demonstration of the near-quantum optimal receiver”, OSA Continuum 3, 3324 (2020) DOI
M. V. Jabir et al., “Energy and bandwidth efficiency optimization of quantum-enabled optical communication channels”, npj Quantum Information 8, (2022) DOI
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Zoo Code ID: quantum_fsk

Cite as:
“Coherent FSK (CFSK) c-q code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022.
@incollection{eczoo_quantum_fsk, title={Coherent FSK (CFSK) c-q code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={} }
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Cite as:

“Coherent FSK (CFSK) c-q code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022.