Abstract
Explicated is a role of the space (Z/dZ)^<2n> equipped with a symplectic bilinear form in quantum information theory. Specifically, quantum error-correcting codes, quantum teleportation, entanglement distillation, quantum cryptography and so on are explained from a unified algebraic point of view. The symplectic bilinear form naturally emerges in the commutation relation for Weyl's ray (projective) representation of (Z/dZ)^<2n>.
