Non-Orthogonality of QAM and Sunflower-like Modulated Coherent-State Signals
The limitations of cloning and discriminating quantum states are related to the non-orthogonality of the states. Hence, understanding the collective features of quantum states is essential for the future development of quantum communications technology. This paper investigates the non-orthogonality...
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MDPI AG
2025-01-01
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| author | Kentaro Kato |
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| description | The limitations of cloning and discriminating quantum states are related to the non-orthogonality of the states. Hence, understanding the collective features of quantum states is essential for the future development of quantum communications technology. This paper investigates the non-orthogonality of different coherent-state signal constellations used in quantum communications, namely phase-shift keying (PSK), quadrature-amplitude modulation (QAM), and a newly defined signal named the sunflower-like (SUN) coherent-state signal. The non-orthogonality index (NOI) and the average probability of correct detection (detection probability) are numerically computed. Results show that PSK NOI increases faster than QAM and SUN as the number of signals increases for a given number of signal photons. QAM and SUN exhibit similar NOI and detection probability, behaving similarly to randomly generated signals for a larger number of signals. Approximation formulas are provided for the detection probability as a function of NOI for each signal type. While similar to QAM, SUN signal offers potential advantages for applications requiring uniform signal-space distribution. The findings provide valuable insights for designing useful quantum signal constellations. |
| format | Article |
| id | doaj-art-e6b2dc8fa5f44236943c860056f09ab0 |
| institution | Kabale University |
| issn | 1099-4300 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
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| series | Entropy |
| spelling | doaj-art-e6b2dc8fa5f44236943c860056f09ab02025-01-24T13:31:44ZengMDPI AGEntropy1099-43002025-01-012713010.3390/e27010030Non-Orthogonality of QAM and Sunflower-like Modulated Coherent-State SignalsKentaro Kato0Quantum ICT Research Institute, Tamagawa University, Tokyo 194-8610, JapanThe limitations of cloning and discriminating quantum states are related to the non-orthogonality of the states. Hence, understanding the collective features of quantum states is essential for the future development of quantum communications technology. This paper investigates the non-orthogonality of different coherent-state signal constellations used in quantum communications, namely phase-shift keying (PSK), quadrature-amplitude modulation (QAM), and a newly defined signal named the sunflower-like (SUN) coherent-state signal. The non-orthogonality index (NOI) and the average probability of correct detection (detection probability) are numerically computed. Results show that PSK NOI increases faster than QAM and SUN as the number of signals increases for a given number of signal photons. QAM and SUN exhibit similar NOI and detection probability, behaving similarly to randomly generated signals for a larger number of signals. Approximation formulas are provided for the detection probability as a function of NOI for each signal type. While similar to QAM, SUN signal offers potential advantages for applications requiring uniform signal-space distribution. The findings provide valuable insights for designing useful quantum signal constellations.https://www.mdpi.com/1099-4300/27/1/30non-orthogonalitydetection probabilitysquare-root measurementsignal constellation |
| spellingShingle | Kentaro Kato Non-Orthogonality of QAM and Sunflower-like Modulated Coherent-State Signals Entropy non-orthogonality detection probability square-root measurement signal constellation |
| title | Non-Orthogonality of QAM and Sunflower-like Modulated Coherent-State Signals |
| title_full | Non-Orthogonality of QAM and Sunflower-like Modulated Coherent-State Signals |
| title_fullStr | Non-Orthogonality of QAM and Sunflower-like Modulated Coherent-State Signals |
| title_full_unstemmed | Non-Orthogonality of QAM and Sunflower-like Modulated Coherent-State Signals |
| title_short | Non-Orthogonality of QAM and Sunflower-like Modulated Coherent-State Signals |
| title_sort | non orthogonality of qam and sunflower like modulated coherent state signals |
| topic | non-orthogonality detection probability square-root measurement signal constellation |
| url | https://www.mdpi.com/1099-4300/27/1/30 |
| work_keys_str_mv | AT kentarokato nonorthogonalityofqamandsunflowerlikemodulatedcoherentstatesignals |