Kato Kentaro
Quantum ICT Research Institute, Tamagawa University, Tokyo 194-8610, Japan.
Entropy (Basel). 2025 Jan 1;27(1):30. doi: 10.3390/e27010030.
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.
量子态克隆与区分的局限性与态的非正交性相关。因此，了解量子态的集体特征对于量子通信技术的未来发展至关重要。本文研究了量子通信中使用的不同相干态信号星座图的非正交性，即相移键控（PSK）、正交幅度调制（QAM）以及一种新定义的名为类向日葵（SUN）相干态信号的信号。通过数值计算得出了非正交性指数（NOI）和正确检测的平均概率（检测概率）。结果表明，对于给定数量的信号光子，随着信号数量的增加，PSK的NOI增长速度比QAM和SUN更快。QAM和SUN表现出相似的NOI和检测概率，对于大量信号，其行为类似于随机生成的信号。针对每种信号类型，给出了检测概率作为NOI函数的近似公式。虽然与QAM相似，但SUN信号在需要均匀信号空间分布的应用中具有潜在优势。这些发现为设计有用的量子信号星座图提供了有价值的见解。
