Generalized security analysis framework for continuous-variable quantum key distribution

Security of practical continuous-variable quantum key distribution is addressed and a security analysis framework, which does not rely on phase-space symmetries of signal states and correlations, is developed. In a general purification-based approach, following optimality of Gaussian collective attacks, it is suggested to find an equivalent generally mixed two-mode state shared between the trusted parties and then purifying it using Bloch-Messiah decomposition. This allows to assess security of the schemes with arbitrary parameters, which can be typically expected in experiments. It also allows to theoretically predict the role of asymmetries of signals and correlations on security of the protocols. The method can be used for security analysis of practical continuous-variable schemes directly from the measured data without any symmetrization assumptions.