HW1 - Problem 3
Problem 3: More bombs
Suppose we repeat the Elitzur-Vaidman bomb experiment but adjust our circuit as follows:
The final measurement is in the standard basis. Recall that
\(R_\theta := \begin{bmatrix}\cos \theta & - \sin \theta \\ \sin \theta & \cos \theta\end{bmatrix}.\)
To recap, the action of the “bomb” gate is the following: - If the bomb is faulty, it does nothing and acts as an identity gate. - If the bomb is not faulty, and the input state is \(\alpha \ket{0} + \beta\ket{1}\), with probability \(|\beta|^2\) the bomb explodes and the experiment ends. With probability \(|\alpha|^2\), nothing happens and the state is reset to \(\ket{0}\).
Just like in class, there are three possible outcomes. - The bomb explodes - We measure \(\ket{0}\) - We measure \(\ket{1}\)
- What are the possible outcomes and probabilities of those outcomes if the bomb is faulty?
- What are the possible outcomes and probabilities of those outcomes if the bomb is not faulty?
- How does this version of the experiment compare to what we did in class? Which is more effective at detecting a bomb that is not faulty without having it explode? Which has a higher probability that the bomb explodes?