Near-optimal coherent state discrimination via continuously labelled non-Gaussian measurements
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AbstractQuantum state discrimination plays a central role in quantum information and communication. For the discrimination of optical quantum states, the two most widely adopted measurement techniques are photon detection, which produces discrete outcomes, and homodyne detection, which produces continuous outcomes. While various protocols using photon detection have been proposed for optimal and near-optimal discrimination between two coherent states, homodyne detection is known to have higher error rates, with its minimum achievable error rate often referred to as the Gaussian limit. In this work, we demonstrate that, despite the fundamental differences between discretely labelled and continuously labelled measurements, continuously labelled non-Gaussian measurements can also achieve near-optimal coherent state discrimination. We design two discrimination protocols that surpass the Gaussian limit: one using non-Gaussian unitary operations with homodyne detection, and another based on orthogonal polynomials. Our results show that photon detection is not required for near-optimal coherent state discrimination and that we can achieve error rates close to the Helstrom bound at low energies with continuously labelled measurements. We also find that our schemes maintain an advantage over the photon detection-based Kennedy receiver for a moderate range of coherent state amplitudes.Featured image: A pictorial representation of the two types of continuously labelled non-Gaussian measurement schemes considered in this work. Type A refers to a non-Gaussian unitary preprocessing of the coherent states followed by Gaussian detection. Type B refers to a continuously labelled non-Gaussian measurement that is unitarily inequivalent to type A.► BibTeX data@article{Moran2026nearoptimalcoherent, doi = {10.22331/q-2026-03-09-2016}, url = {https://doi.org/10.22331/q-2026-03-09-2016}, title = {Near-optimal coherent state discrimination via continuously labelled non-{G}aussian measurements}, author = {Moran, James and Kechrimparis, Spiros and Kwon, Hyukjoon}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2016}, month = mar, year = {2026} }► References [1] S. M. Barnett and S. Croke, Quantum state discrimination, Adv. Opt. Photon. 1, 238–278 (2009). https://doi.org/10.1364/AOP.1.000238 [2] J. Bae and L.-C. Kwek, Quantum state discrimination and its applications, J. Phys. A Math. Theor. 48, 083001 (2015). https://doi.org/10.1088/1751-8113/48/8/083001 [3] M. A. Nielsen and I. L. 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Kahn, A. Gnauck, J. Veselka, S. Korotky, and B. Kasper, 4-Gb/s PSK homodyne transmission system using phase-locked semiconductor lasers, IEEE Photonics Technology Letters 2, 285–287 (1990). https://doi.org/10.1109/68.53264 [8] C. Wittmann, M. Takeoka, K. N. Cassemiro, M. Sasaki, G. Leuchs, and U. L. Andersen, Demonstration of near-optimal discrimination of optical coherent states, Phys. Rev. Lett. 101, 210501 (2008). https://doi.org/10.1103/PhysRevLett.101.210501 [9] M. Takeoka and M. Sasaki, Discrimination of the binary coherent signal: Gaussian-operation limit and simple non-Gaussian near-optimal receivers, Phys. Rev. A 78, 022320 (2008). https://doi.org/10.1103/PhysRevA.78.022320 [10] R. Han, J. A. Bergou, and G. Leuchs, Near optimal discrimination of binary coherent signals via atom–light interaction, New J. Phys. 20, 043005 (2018). https://doi.org/10.1088/1367-2630/aab2c5 [11] J. S. Sidhu, M. S. Bullock, S. Guha, and C. 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Houhou, Linear and quadratic reservoir engineering of non-Gaussian states, Phys. Rev. A 100, 013831 (2019). https://doi.org/10.1103/PhysRevA.100.013831Cited byCould not fetch Crossref cited-by data during last attempt 2026-03-09 11:38:19: Could not fetch cited-by data for 10.22331/q-2026-03-09-2016 from Crossref. This is normal if the DOI was registered recently. Could not fetch ADS cited-by data during last attempt 2026-03-09 11:38:19: No response from ADS or unable to decode the received json data when getting the list of citing works.This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions. AbstractQuantum state discrimination plays a central role in quantum information and communication. For the discrimination of optical quantum states, the two most widely adopted measurement techniques are photon detection, which produces discrete outcomes, and homodyne detection, which produces continuous outcomes. While various protocols using photon detection have been proposed for optimal and near-optimal discrimination between two coherent states, homodyne detection is known to have higher error rates, with its minimum achievable error rate often referred to as the Gaussian limit. In this work, we demonstrate that, despite the fundamental differences between discretely labelled and continuously labelled measurements, continuously labelled non-Gaussian measurements can also achieve near-optimal coherent state discrimination. We design two discrimination protocols that surpass the Gaussian limit: one using non-Gaussian unitary operations with homodyne detection, and another based on orthogonal polynomials. Our results show that photon detection is not required for near-optimal coherent state discrimination and that we can achieve error rates close to the Helstrom bound at low energies with continuously labelled measurements. We also find that our schemes maintain an advantage over the photon detection-based Kennedy receiver for a moderate range of coherent state amplitudes.Featured image: A pictorial representation of the two types of continuously labelled non-Gaussian measurement schemes considered in this work. Type A refers to a non-Gaussian unitary preprocessing of the coherent states followed by Gaussian detection. Type B refers to a continuously labelled non-Gaussian measurement that is unitarily inequivalent to type A.► BibTeX data@article{Moran2026nearoptimalcoherent, doi = {10.22331/q-2026-03-09-2016}, url = {https://doi.org/10.22331/q-2026-03-09-2016}, title = {Near-optimal coherent state discrimination via continuously labelled non-{G}aussian measurements}, author = {Moran, James and Kechrimparis, Spiros and Kwon, Hyukjoon}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2016}, month = mar, year = {2026} }► References [1] S. M. Barnett and S. Croke, Quantum state discrimination, Adv. Opt. Photon. 1, 238–278 (2009). https://doi.org/10.1364/AOP.1.000238 [2] J. Bae and L.-C. Kwek, Quantum state discrimination and its applications, J. Phys. A Math. Theor. 48, 083001 (2015). https://doi.org/10.1088/1751-8113/48/8/083001 [3] M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information: 10th Anniversary Edition (Cambridge University Press, 2010). https://doi.org/10.1017/CBO9780511976667 [4] S. Pirandola, U. L. Andersen, L. Banchi, M. Berta, D. Bunandar, R. Colbeck, D. Englund, T. Gehring, C. Lupo, C. Ottaviani, J. L. Pereira, M. Razavi, J. S. Shaari, M. Tomamichel, V. C. Usenko, G. Vallone, P. Villoresi, and P. Wallden, Advances in quantum cryptography, Adv. Opt. Photon. 12, 1012–1236 (2020). https://doi.org/10.1364/AOP.361502 [5] J. S. Sidhu, S. K. Joshi, M. Gündoğan, T. Brougham, D. Lowndes, L. Mazzarella, M. Krutzik, S. Mohapatra, D. Dequal, G. Vallone, P. Villoresi, A. Ling, T. Jennewein, M. Mohageg, J. G. Rarity, I. Fuentes, S. Pirandola, and D. K. L. Oi, Advances in space quantum communications, IET Quantum Commun. 2, 182–217 (2021). https://doi.org/10.1049/qtc2.12015 [6] C. W. Helstrom, Quantum detection and estimation theory, J. Stat. Phys. 1, 231–252 (1969). https://doi.org/10.1007/BF01007479 [7] J. Kahn, A. Gnauck, J. Veselka, S. Korotky, and B. Kasper, 4-Gb/s PSK homodyne transmission system using phase-locked semiconductor lasers, IEEE Photonics Technology Letters 2, 285–287 (1990). https://doi.org/10.1109/68.53264 [8] C. Wittmann, M. Takeoka, K. N. Cassemiro, M. Sasaki, G. Leuchs, and U. L. Andersen, Demonstration of near-optimal discrimination of optical coherent states, Phys. Rev. Lett. 101, 210501 (2008). https://doi.org/10.1103/PhysRevLett.101.210501 [9] M. Takeoka and M. Sasaki, Discrimination of the binary coherent signal: Gaussian-operation limit and simple non-Gaussian near-optimal receivers, Phys. Rev. A 78, 022320 (2008). https://doi.org/10.1103/PhysRevA.78.022320 [10] R. Han, J. A. Bergou, and G. Leuchs, Near optimal discrimination of binary coherent signals via atom–light interaction, New J. Phys. 20, 043005 (2018). https://doi.org/10.1088/1367-2630/aab2c5 [11] J. S. Sidhu, M. S. Bullock, S. Guha, and C. Lupo, Linear optics and photodetection achieve near-optimal unambiguous coherent state discrimination, Quantum 7, 1025 (2023). https://doi.org/10.22331/q-2023-05-31-1025 [12] A. Warke, J. Nötzel, K. Takase, W. Asavanant, H. Nagayoshi, K. Fukui, S. Takeda, A. Furusawa, and P. van Loock, Photonic quantum receiver attaining the Helstrom bound, arXiv:2410.21800 (2024). https://doi.org/10.48550/arXiv.2410.21800 arXiv:2410.21800 [13] M. Sasaki, T. S. Usuda, and O. Hirota, Physical aspect of the improvement of quantum-noise characteristics caused by unitary transformation with a nonlinear optical medium, Phys. Rev. A 51, 1702–1705 (1995). https://doi.org/10.1103/PhysRevA.51.1702 [14] T. S. Usuda and O. Hirota, An example of a received quantum state controller by optical kerr effect, in Quantum Communications and Measurement (Springer US, Boston, MA, 1995) pp. 419–427. https://doi.org/10.1007/978-1-4899-1391-3_41 [15] S. J. Dolinar, An optimum receiver for the binary coherent state quantum channel, MIT Res. Lab. Elec. Q. Prog. Rep. 111, 115 (1973). http://hdl.handle.net/1721.1/56414 [16] M. Sasaki and O. Hirota, Optimum decision scheme with a unitary control process for binary quantum-state signals, Phys. Rev. A 54, 2728–2736 (1996). https://doi.org/10.1103/PhysRevA.54.2728 [17] R. J. Glauber, The quantum theory of optical coherence, Phys. Rev. 130, 2529–2539 (1963). https://doi.org/10.1103/PhysRev.130.2529 [18] E. C. G. Sudarshan, Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams, Phys. Rev. Lett. 10, 277–279 (1963). https://doi.org/10.1103/PhysRevLett.10.277 [19] C. Weedbrook, S. Pirandola, R. García-Patrón, N. J. Cerf, T. C. Ralph, J. H. Shapiro, and S. Lloyd, Gaussian quantum information, Rev. Mod. Phys. 84, 621–669 (2012). https://doi.org/10.1103/RevModPhys.84.621 [20] G. Adesso, S. Ragy, and A. R. 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Houhou, Linear and quadratic reservoir engineering of non-Gaussian states, Phys. Rev. A 100, 013831 (2019). https://doi.org/10.1103/PhysRevA.100.013831Cited byCould not fetch Crossref cited-by data during last attempt 2026-03-09 11:38:19: Could not fetch cited-by data for 10.22331/q-2026-03-09-2016 from Crossref. This is normal if the DOI was registered recently. Could not fetch ADS cited-by data during last attempt 2026-03-09 11:38:19: No response from ADS or unable to decode the received json data when getting the list of citing works.This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.