We have constructed a theory of dual canonical formalism to study the quantum competing systems. In such a system, as the relationship between current and voltage of each, we assumed the duality condition. We considered competing systems of two types. One type is composed of a sandwich structure with a superconductor (SC)/superinsulator (SI)/SC junction, and its dual junction consists of a sandwich structure formed by the SI/SC/SI junction. The other type of system consists of a sandwich structure formed by the SC/FM (ferromagnet)/SC junction, and its dual junction consists of a sandwich structure formed by the FM/SC/FM junction (spin Josephson junctions). We derived the relationship between the phase and the number of particles in a dual system. As an application of the dual competitive systems, we introduce a quantum spin transistor.