Can Measurements Determine Pure vs. Mixture Ensembles in Quantum Theory?

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SUMMARY

This discussion centers on the differentiation between pure and mixture ensembles in quantum theory, referencing Giancarlo Ghirardi's reasoning. Participants explore the implications of measurements on observables in superposition states, specifically citing the double-slit experiment and a recent entanglement experiment involving two diamonds. The conversation concludes that measurements indeed collapse superpositions, leading to definitive outcomes such as A+1 or A-1 based on the observable measured.

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  • Knowledge of the double-slit experiment and its implications
  • Basic concepts of quantum entanglement and observable states
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Just trying to follow Giancarlo Ghirardi reasoning in his book about differentiating between pure and mixture esembles.

Is it possible to perform a measurement on an observable that, if it were in a superposition, a certain value would return?
 
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StevieTNZ said:
Just trying to follow Giancarlo Ghirardi reasoning in his book about differentiating between pure and mixture esembles.

Is it possible to perform a measurement on an observable that, if it were in a superposition, a certain value would return?

Yes. There is the hoary double-slit experiment. If you insist on a single measurement, the recent experiment on entanglement that involved two diamonds qualifies.
 
Ah ok.

Because X would return if the state was in |A+1>+|A-1>, and Y would return if the state was in |A+1>-|A-1>.

After measurement of the observable, would either X or Y return, plus a definite A+1 or A-1? I guess when the measurement is done, its checking to see if its in a superposition, but once measurement is over, you'd expect the superposition to have collapsed.
 

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