Security Thresholds of Multicarrier Continuous-Variable Quantum Key Distribution

We prove the secret key rate formulas and derive security threshold parameters of multi-carrier continuous-variable quantum key distribution (CVQKD). In a multicarrierCVQKD scenario, the Gaussian input quantum states of the legal parties are granulatedinto Gaussian subcarrier CVs (continuous-variables). The multicarrier communicationformulates Gaussian sub-channels from the physical quantum channel, each dedicated tothe transmission of a subcarrier CV. The Gaussian subcarriers are decoded by a unitaryCV operation, which results in the recovered single-carrier Gaussian CVs. We derive theformulas through the AMQD (adaptive multicarrier quadrature division) scheme, theSVD-assisted (singular value decomposition) AMQD, and the multiuser AMQD-MQA(multiuser quadrature allocation). We prove that the multicarrier CVQKD leads to im-proved secret key rates and higher tolerable excess noise in comparison to single-carrierCVQKD. We derive the private classical capacity of a Gaussian sub-channel and the secu-rity parameters of an optimal Gaussian collective attack in the multicarrier setting. Wereveal the secret key rate formulas for one-way and two-way multicarrier CVQKD proto-cols, assuming homodyne and heterodyne measurements and direct and reverse reconcilia-tion. The results reveal the physical boundaries of physically allowed Gaussian attacks ina multicarrier CVQKD scenario and confirm that the improved transmission rates lead toenhanced secret key rates and security thresholds.