Quadrature Entanglement in Cascaded Down Conversion for Multiparty Continuous Variable Quantum Key Distribution

A multiparty continuous-variable quantum key distribution (CVQKD) algorithm still remains to be shown, which is the goal of this paper. In contrast to pair-wise discrete quantum key distribution, multiparty CVQKD has the advantage of better detection and measurement with homodyne detectors and higher efficiency quantum networks. We provide a rigorous theoretical argument in addition to a discussion on the relevant experimental conditions for the proposed protocol. Said protocol involves utilizing the quadrature entanglement and phase correlations in noncollinear cascaded spontanous parametric down conversions (SPDC) to share secure keys between N parties involving the quadrature measurement of coherent photon modes. We then build on this to describe the symmetries of potential quantum networks based off the protocol, aiming to maximize the connectivity and security over a single quantum key distribution. We evaluate the protocol in a variety of situations, finding that the protocol does not degrade in security, only efficiency as the number of parties increases as a result of the SPDC conversion efficiencies in different materials.