Secret key rate proof of multicarrier continuous‐variable quantum key distribution

• Published in: International journal of communication systems Vol. 32; no. 4
• Main Authors: Gyongyosi, Laszlo, Imre, Sandor
• Format: Journal Article
• Language: English
• Published: Chichester Wiley Subscription Services, Inc 10.03.2019
• Subjects: Continuity (mathematics); Granulation; Parameters; Public Key Infrastructure; Quantum cryptography; Security; Singular value decomposition; Subcarriers
• ISSN: 1074-5351; 1099-1131
• DOI: 10.1002/dac.3865

Summary We prove the secret key rate formulas and derive security threshold parameters of multicarrier continuous‐variable quantum key distribution CVQKD. In a multicarrier CVQKD scenario, the Gaussian input quantum states of the legal parties are granulated into Gaussian subcarrier continuous variables (CVs). The multicarrier communication formulates Gaussian subchannels from the physical quantum channel, each dedicated to the transmission of a subcarrier CV. The Gaussian subcarriers are decoded by a unitary CV operation, which results in the recovered single‐carrier Gaussian CVs. We derive the formulas through the adaptive multicarrier quadrature division (AMQD) scheme, the singular value decomposition (SVD)–assisted AMQD, and the multiuser AMQD multiuser quadrature allocation (MQA). We prove that the multicarrier CVQKD leads to improved secret key rates and higher tolerable excess noise in comparison with single‐carrier CVQKD. We derive the private classical capacity of a Gaussian subchannel and the security parameters of an optimal Gaussian collective attack in the multicarrier setting. We reveal the secret key rate formulas for one‐way and two‐way multicarrier CVQKD protocols, assuming homodyne and heterodyne measurements and direct and reverse reconciliation. The results reveal the physical boundaries of physically allowed Gaussian attacks in a multicarrier CVQKD scenario and confirm that the improved transmission rates lead to enhanced secret key rates and security thresholds. We prove the secret key rate formulas and derive security threshold parameters of multicarrier continuous‐variable quantum key distribution (CVQKD). We derive the formulas through the adaptive multicarrier quadrature division (AMQD) scheme, the singular value decomposition (SVD)–assisted AMQD, and the multiuser AMQD multiuser quadrature allocation (MQA). We derive the private classical capacity of a Gaussian subchannel and the security parameters. We prove that the multicarrier CVQKD leads to improved secret key rates and higher tolerable excess noise in comparison with single‐carrier CVQKD.