If the particles are indistinguishable, however, there are only N +1 different configurations. If there are K particles in state | 1 ⟩ ⟩ , there are N − K particles in state | 0 ⟩ ⟩ . Whether any particular particle is in state | 0 ⟩ ⟩ or in state | 1 ⟩ ⟩ cannot be determined, so each value of K determines a unique quantum state for the whole system.