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

[StevieTNZ]

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?

 

[PatrickPowers]

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.

 

[StevieTNZ]

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.