Phase-space representation of quantum state vectors is a formulation of quantum mechanics elaborating the phase-space formulation with a Hilbert space. It "is obtained within the framework of the relative-state formulation. For this purpose, the Hilbert space of a quantum system is enlarged by introducing an auxiliary quantum system. Relative-position state and relative-momentum state are defined in the extended Hilbert space of the composite quantum system and expressions of basic operators such as canonical position and momentum operators, acting on these states, are obtained." Thus, it is possible to assign a meaning to the wave function in phase space, ψ ψ ( x , p , t ) , as a quasiamplitude, associated to a quasiprobability distribution.