Suppose you have a source that produces atoms in an unknown spin-half state | a). Design...

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Suppose you have a source that produces atoms in an unknown spin-half state | a). Design two experiments to determine |a). Describe your designs (with the aid of pictures, if they help) and explain concisely why the experiments would work. (a) In the first experiment, you are given a beam splitter whose orientation is freely tunable to any direction. Design an experiment that takes advantage of this freely-tunable orientation to determine | a), drawing inspiration from lecture 8. (b) In the second experiment, you are given three beam splitters with orientations fixed to x, and respectively. With this restricted freedom, design an experiment to determine | a), drawing inspiration from problem I in this assignment, and the interpretation of an expectation value as an averaged measurement outcome. Suppose you have a source that produces atoms in an unknown spin-half state | a). Design two experiments to determine |a). Describe your designs (with the aid of pictures, if they help) and explain concisely why the experiments would work. (a) In the first experiment, you are given a beam splitter whose orientation is freely tunable to any direction. Design an experiment that takes advantage of this freely-tunable orientation to determine | a), drawing inspiration from lecture 8. (b) In the second experiment, you are given three beam splitters with orientations fixed to x, and respectively. With this restricted freedom, design an experiment to determine | a), drawing inspiration from problem I in this assignment, and the interpretation of an expectation value as an averaged measurement outcome.