This state is separable if there exist vectors [c^A_i], [c^B_j] so that c_{ij}= c^A_i c^B_j, yielding |\psi\rangle_A = \sum_{i} c^A_{i} |i\rangle_A and |\phi\rangle_B = \sum_{j} c^B_{j} |j\rangle_B. It is inseparable if for any vectors [c^A_i],[c^B_j] at least for one pair of coordinates c^A_i,c^B_j we have c_{ij} \neq c^A_ic^B_j. If a state is inseparable, it is called an 'entangled state'.
