BPSK c-q code 


Coherent-state c-q binary code encoding into two coherent states \(|\pm\alpha\rangle\) for complex \(\alpha\). A shifted version, with codewords \(\{|0\rangle,|\alpha\rangle\}\), is called binary amplitude modulation (BAM), The three-state subcode \(\{|\alpha,\alpha\rangle,|-\alpha,\alpha\rangle,|\alpha,-\alpha\rangle\}\) of two-mode BPSK is called the single-degeneracy code [1].


The single-degeneracy code yields an improved PIE by \(2.8\%\) over BPSK [2] (see [1]).


Linear-optical quantum receiver [3].Kennedy receiver [4,5].Photon-number resolving detector [6].Non-Gaussian near-optimal receiver [5].Multi-stage quantum receiver [7].


Linear-optical quantum receiver [3].Homodyne receiver [8].Kennedy receiver [8,9].Photon-number resolving detector [6].Communication over dephasing [10], time-varying phase-noise [11], and thermal-noise [12] channels.Adaptive decoder using displacements and photon detection [13].BPQM detector on a BPSK-modulated tree code [14].



  • Binary PSK (BPSK) code — BPSK (BPSK c-q) codes are used to transmit classical information using antipodal coherent states over classical (quantum) channels.
  • Two-component cat code — BPSK c-q (two-component cat) codes are used to transmit classical (quantum) information using (superpositions of) antipodal coherent states over quantum channels.
  • On-off keyed (OOK) c-q code — OOK c-q codewords are related to BPSK c-q codewords by a displacement in phase space.


S. Guha, “Structured Optical Receivers to Attain Superadditive Capacity and the Holevo Limit”, Physical Review Letters 106, (2011) arXiv:1101.1550 DOI
J. R. Buck, S. J. van Enk, and C. A. Fuchs, “Experimental proposal for achieving superadditive communication capacities with a binary quantum alphabet”, Physical Review A 61, (2000) DOI
K. Tsujino et al., “Quantum Receiver beyond the Standard Quantum Limit of Coherent Optical Communication”, Physical Review Letters 106, (2011) arXiv:1103.5592 DOI
Kennedy, Robert S. "A near-optimum receiver for the binary coherent state quantum channel." Quarterly Progress Report 108 (1973): 219-225.
M. Takeoka and M. Sasaki, “Discrimination of the binary coherent signal: Gaussian-operation limit and simple non-Gaussian near-optimal receivers”, Physical Review A 78, (2008) arXiv:0706.1038 DOI
M. T. DiMario and F. E. Becerra, “Robust Measurement for the Discrimination of Binary Coherent States”, Physical Review Letters 121, (2018) arXiv:1807.05199 DOI
D. Sych and G. Leuchs, “Practical Receiver for Optimal Discrimination of Binary Coherent Signals”, Physical Review Letters 117, (2016) arXiv:1404.5033 DOI
C. Wittmann et al., “Demonstration of Near-Optimal Discrimination of Optical Coherent States”, Physical Review Letters 101, (2008) arXiv:0809.4953 DOI
M. L. Shcherbatenko et al., “Sub-shot-noise-limited fiber-optic quantum receiver”, Physical Review A 101, (2020) arXiv:1911.08932 DOI
M. T. DiMario et al., “Optimized communication strategies with binary coherent states over phase noise channels”, npj Quantum Information 5, (2019) arXiv:1907.12515 DOI
M. T. DiMario and F. E. Becerra, “Phase tracking for sub-shot-noise-limited receivers”, Physical Review Research 2, (2020) DOI
R. Yuan et al., “Optimally Displaced Threshold Detection for Discriminating Binary Coherent States Using Imperfect Devices”, (2020) arXiv:2007.11109
M. T. DiMario and F. E. Becerra, “Demonstration of optimal non-projective measurement of binary coherent states with photon counting”, npj Quantum Information 8, (2022) arXiv:2207.12234 DOI
C. Delaney et al., “Demonstration of a quantum advantage by a joint detection receiver for optical communication using quantum belief propagation on a trapped-ion device”, Physical Review A 106, (2022) arXiv:2102.13052 DOI
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Zoo Code ID: quantum_bpsk

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

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