I'm stuck on the following problem:

Suppose we are given a qubit |q> in an unknown state, but we know it is either |0> or

1/sqrt(2)(|0> + |1>). We would like to devise a circuit to determine, with certainty,

which of the two is the case, using any number of unitary and measurement

operations.

Either explain how to construct such a circuit, or prove that no such circuit is

possible.

Can somebody give me a suggestion for tackling this? My intuition tells me that it shouldn't be possbile and I'd like to prove by contradiction, but I haven't yet been able to come up with anything.

Thanks