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Observing = learning outcome
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Because after observing all possibilities collapse to one.
Example:
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The point here is that the result doesn't change if we observe at any point in the process!
Measuring a quantum system
Given a quantum state \psi \in \mathbb{C}^n we will
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BUT!!! Measuring a quantum state CHANGES THE SYSTEM!!!
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Elitzur-Vaidman bomb tester
Given a box we want to determine whether it contains a bomb. To test, a photon can be send through the box.
- if the bomb detects a photon it explodes!
- if no bomb is present nothing happens
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Beam Splitter
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A beam splitter is a semi transparent mirror.
Photons entering from up can come out on the up or down path - analog for down
Quantum mechanically it could come in a superposition between up and down
\begin{pmatrix} \alpha \\ \beta \end{pmatrix} a = amplitude of up, b = amplitude of down
And it would exit the beam splitter in a superposition between up and down again
\begin{pmatrix} \gamma \\ \delta \end{pmatrix} gamma = up, delta = down
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The bomb tester now looks like this:
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