Bad Qubits — Learn Quantum by Doing

Multiple choice

The no-cloning proof assumes a unitary

U

with

U|\psi\rangle|0\rangle = |\psi\rangle|\psi\rangle

for every state. Taking the inner product of this relation applied to two states

|\psi\rangle

and

|\phi\rangle

yields which equation, and what does it imply?

$\langle\psi|\phi\rangle = \langle\psi|\phi\rangle^2$ , forcing the overlap to be 0 or 1, so no $U$ clones arbitrary states
$\langle\psi|\phi\rangle = 2\langle\psi|\phi\rangle$ , which holds for all states, so cloning is always allowed
$\langle\psi|\phi\rangle^2 = 1$ , proving all states are identical
$\langle\psi|\phi\rangle = 0$ for all states, proving every pair of states is orthogonal