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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Quantum quadrature amplitude modulation system and its applicability to coherent-state quantum cryptography

Kentaro Kato, Osamu Hirota

Published Aug 14, 2005• 43 citations
Publisher

Abstract

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.

DOI
10.1117/12.618719

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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.
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Quantum communication systems exchange information between a source and a destination by encoding such information into quantum states according to modulation techniques. The design of quantum modulation techniques, including quantum quadrature amplitude modulation (QAM), requires choosing and characterizing quantum states. This paper explores the use of non-Gaussian photon-added Gaussian states (PAGSs) for quantum QAM communications. First, we characterize pure PAGSs in the Fock space and derive a closed-form expression for their inner product. Then, we develop a quantum QAM technique employing PAGSs. In particular, we show how to construct quantum QAM constellations of PAGSs. Finally, we evaluate the performance of the developed quantum QAM technique with PAGSs, when a square root measurement (SRM) receiver is employed, and compare such performance with that of existing coherent states. Results show that PAGSs can provide a performance gain with respect to coherent states.
A unified treatment of typical optical modulation formats is given toward a future development of the quantum enigma cipher. In our analysis, the intensity shift keying (ISK), amplitude shift keying (ASK), phase shift keying (PSK), and quadrature amplitude modulation (QAM) coherent state signals are compared in terms of the masking number of potential signals through the numerical calculations of the square-root measurement. Through this comparison, we see that the use of ISK coherent state signal is the best choice for cryptographic purpose among these formats in achieving an appropriate balance between the number of signal photons and the number of quantum state signals.
A quantum noise stream cipher scheme (QNSC) based on triangular quadrature amplitude modulation (TQAM) and the secret probabilistic shaping (SPS) is studied. Compared with rectangular quadrature amplitude modulation (QAM), TQAM is a more compact symmetrical structure, which results in better transmission performance and greater noise masking number. Then, SPS is realized, where the probabilistic shaping information as the secret key is masked into noise and transmitted with the encrypted signal simultaneously. The combination of SPS and QNSC makes it impossible for an attacker to obtain the ciphertext, which enhances the security of QNSC scheme without introducing additional key. TQAM and probabilistic shaping improve the transmission performance of QNSC scheme. Under 7% forward error correction (FEC) threshold in back-to-back system, compared with QAM/QNSC systems, TQAM/QNSC provides an OSNR gain of ∼ 0.6 dB, and SPS-TQAM/QNSC provides an OSNR gain of ∼ 1.2 dB. The proposed scheme is demonstrated with the net data rate of 34.28 Gbit/s over 140 km single-span standard single mode fiber.
A ciphertext mapping method based on Gray code is proposed to improve the security of quantum noise stream cipher (QNSC). The experiment is conducted in 1024 × 1024 -quadrature amplitude modulation (QAM) coherent optical communication system over 300 km. Experimental results verify that the proposed scheme does not affect the transmission performance. Meanwhile, the performance analysis reveals that the attacker's bit error rate (BER) increases to about 0.5 per bit position per symbol. The advantage of proposed scheme is that QNSC makes use of basis with fewer bits for encryption/decryption.