It isn't by definition, presuming the relationship between quantum mechanics and reality. You can have a _two particle_ state and a _one particle state_ with no

It isn't by definition, presuming the relationship between quantum mechanics and reality. You can have a _two particle_ state and a _one particle state_ with non-trivial probability of being in two places. They are distinct things. The key idea here (and really, in Quantum Mechanics generally) is that superpositions are important things in the theory. This is the statement that if you have a wave function for one situation and another wave function for another than the sum of the two is also, necessarily, a valid wave function for a physically realizable system. This is different from a classical probability. Suppose we simply don't know whether the baseball was fired from HERE or from THERE. In a classical situation, we can carry forward our understanding of the situation in time by simply calculating what the classical particles would do independently. In quantum mechanics the mechanics are of the wave function itself, not of the things we measure. We cannot get the right answer by imagining first that we measure the particle in one location and calculate forward and then by imagining we measure the particle in another and calculating forward and then adding the results. It isn't how the theory works. We must time evolve the wave function to predict the statistical behavior of measurement in the future.