The Bicomplex Tensor Product, a Bicomplex Choi Theorem and Applications

Abstract

In this paper we extend the concept of tensor product to the bicomplex case and use it to prove the bicomplex counterpart of the classical Choi theorem in the theory of complex matrices and operators. The concept of hyperbolic tensor product is also discussed, and we link these results to the theory of quantum channels in the bicomplex and hyperbolic case, as well as applications to bicomplex digital signal processing.