Indeed, this is one of the hallmarks of entanglement in quantum mechanics. Suppose you have two qubits, one of which can be in the states |0> and |1> and the o

Indeed, this is one of the hallmarks of entanglement in quantum mechanics. Suppose you have two qubits, one of which can be in the states |0> and |1> and the other which can be in the states |a> and |b> (an unconventional choice, but clearer when there's no TeX). If |psi> = some superposition of |0> and |1> and |chi> = some superposition of |a> and |b> then there is a class of states |psi> (tensor product) |chi>. These states factorize, and thus the two qubits are not entangled. However, there are states like |bell> = |0> (tensor) |a> + |1> (tensor) |b> which do not factorize. We call these states entangled.