Comments (2)
I believe "inner product" in Wolfram Alpha does not match that used in quantum computing. The one in Wolfram Alpha just performs pairwise multiplication of the input vectors and adds the results, while in quantum computing you multiply one vector by the adjoint of the other, taking complex conjugates of the amplitudes of one of the states. The matching Wolfram Alpha query would be this one, with the amplitudes of the second vector being e^(-4πi/3) and e^(-2πi/3) - then the result is 0 indeed.
Additionally, the solution to this task confirms that the states are orthogonal - otherwise we wouldn't be able to distinguish them perfectly!
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That makes sense!
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