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

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In summary, the conversation discusses Giancarlo Ghirardi's reasoning on differentiating between pure and mixture ensembles. The question is raised about whether it is possible to perform a measurement on an observable that would return a certain value if the state was in a superposition. The example of the double-slit experiment and a recent experiment on entanglement are mentioned. The concept of collapse of a superposition after measurement is also discussed.
  • #1
StevieTNZ
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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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  • #2
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.
 
  • #3
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.
 

1. Can this measurement be done with the equipment we have?

The answer to this question depends on the specific measurement and the equipment available. It is important to carefully evaluate the capabilities and limitations of the equipment before attempting the measurement. If the equipment is not suitable, alternative methods or equipment may need to be considered.

2. What is the accuracy and precision of this measurement?

The accuracy and precision of a measurement are important factors to consider. Accuracy refers to how close the measurement is to the true value, while precision refers to how close multiple measurements are to each other. The accuracy and precision of a measurement can be affected by factors such as equipment calibration, human error, and environmental conditions.

3. Are there any potential sources of error in this measurement?

It is important to identify and address potential sources of error in a measurement. These can include environmental factors, equipment limitations, and human error. By understanding and minimizing potential sources of error, the accuracy and reliability of the measurement can be improved.

4. What units should be used for this measurement?

The units used for a measurement should be carefully considered and chosen based on the quantity being measured and the desired level of precision. It is important to use consistent units throughout the measurement process to ensure accuracy and avoid confusion.

5. How many measurements should be taken for this experiment?

The number of measurements to be taken for an experiment will depend on the desired level of precision and the variability of the data. Generally, a larger number of measurements will lead to a more accurate representation of the data, but the specific number should be determined based on the specific experiment and its goals.

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