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Is it possible to explicitly prepare a single system in a state other than the eigenstate?

For example, to prepare a particle in such a way that it will show spin up 80% of the time, and down 20% of the time?

I am asking for a single system. One way I know this is achieved is to take a 100 particles, 80 in spin up, and 20 in spin down, and pick one, which may have this state. However is it possible to design a single particle to do this? (Or any system where this question is applicable for that matter)

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  • $\begingroup$ Prepare a neutral pion. It will decay to two photons whose spins are oppositely entangled. $\endgroup$
    – probably_someone
    Commented May 22, 2018 at 16:51

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Yes. Take a particle and measure its spin along some axis. Then take a second detector and put it after at some angle $\alpha$ compared to the first one. The second detector will detect $\cos^2 \alpha$ particles with spin up and $\sin^2 \alpha$ with spin down. So if you want an $80\%$ up and $20\%$ down you need an angle of

$$\alpha = \arccos(\sqrt{0.8})\approx 26.6^{\circ}$$

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