Every male person, upon whom has been imposed the judgment of death, shall be delivered to the warden of the California state prison designated by the department for the execution of the death penalty. The inmate shall be kept in a California prison until execution of the judgment. The department may transfer the inmate to another prison which it determines to provide a level of security sufficient for that inmate. The inmate shall be returned to the prison designated for execution of the death penalty after an execution date has been set.