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Entropy

Non-Orthogonality of QAM and Sunflower-like Modulated Coherent-State Signals

Kentaro Kato

Published Jan 1, 2025• 1 citation

Abstract

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.

DOI: 10.3390/e27010030

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We analyze the performance of the error probability and the mutual information for quadrature amplitude modulation (QAM) and phase-shift keying systems based on quantum detection theory. It is shown that the quantum receiver called square root measurement gives about 5.7 dB improvement in power in comparison with the classical one. Furthermore, we show that the quantum QAM system can achieve the same reliability as the conventional intensity modulation-direct detection (IM-DD) system with almost equal power, compressing the required bandwidth, while the reliability is degraded in general.

The quadrature amplitude modulation (QAM) signal of coherent state of light is applied to the quantum stream cipher by Y-00 protocol. We first discuss on the performance of the square-root measurement (SRM) for the QAM signals in comparison with the optimum receiver. It is shown that the quantum stream cipher with the QAM signals is designed by using the SRM, taking account of the ciphertext-only attack and the known/chosen plain attack. Furthermore, the modification of the quantum stream cipher with the QAM signals is considered.

We numerically evaluate the wavelength division multiplexing (WDM) data transmission of coherent phase-shift keying (PSK) and quadrature amplitude modulation (QAM) signals in optical fiber communication and deep-space communication channels with conventional homodyne-based(dyne-type) detections and various quantum detection strategies. We show the quantitative gap between these detection strategies and especially in the quantum-limited region where the quantum noise seriously limits the transmission rate. For an extremely weak signal input power, there is a crucial gap between the capacity limit and the transmission rates of the WDM system with dyne-type detections. We show that this gap is filled by applying a collective square root detection (SRD) only for each channel, not necessary for quantum collective decoding among WDM channels.