# Repeating measurement of observables?

• iharuyuki
In summary: By assumption, the states of F and G are eigenstates of the operator for the two observables. Therefore, Alice can predict what Bob will measure.
iharuyuki
I have a question on my homework set and I'm not sure the principle behind it:
1. Alice measured an observable F (a matrix) and passed the measured system immediately to another experimentalist, Bob, who is going to measure another observable G. Alice claims that she can deduce the experiment outcome of Bob without Bob telling her what his outcome is. Can she really do that?

2. Given the observables F and G, suppose Alice measures an observable G first then passes the measured system to Bob, who then measures F. Can Alice deduce Bob's outcome? Can Bob's deduce Alice's?F=
1 0 0
0 1 0
0 0 4

G=
1 0 0
0 5 0
0 0 6

I apologize for the poorly formatted matrices. I'm not sure how to put them in LaTeX.1. I believe Alice cannot deduce the outcome of Bob's experiment (Question: what does "deduce" imply in this context?) because upon measurement the system will collapse into one of its eigenstates which each have a probability of occurring. Thus Alice will not be able to deduce with certainty the result that Bob measured.

2. I believe the same principle applies and neither of them can deduce each other's outcome.

Are my answers correct? Thank you.

iharuyuki said:
1. I believe Alice cannot deduce the outcome of Bob's experiment (Question: what does "deduce" imply in this context?) because upon measurement the system will collapse into one of its eigenstates which each have a probability of occurring. Thus Alice will not be able to deduce with certainty the result that Bob measured.

2. I believe the same principle applies and neither of them can deduce each other's outcome.

Are my answers correct? Thank you.
No, but really all you're doing is asserting your answers here. Alice makes a measurement, and as a result, the system collapses into some state. Somehow from there, you jumped to Alice can't deduce what Bob will measure. What's your reasoning here?

vela said:
No, but really all you're doing is asserting your answers here. Alice makes a measurement, and as a result, the system collapses into some state. Somehow from there, you jumped to Alice can't deduce what Bob will measure. What's your reasoning here?

Thank you. Let me try again.

1. Once Bob's conducts his experiment, upon measurement, the system will collapse into one of its eigenstates which each have a probability of occurring. Since there is a certain probability of each state occurring, and each measurement could possibly result in a different eigenstate, there is no guarantee that Alice's method of deduction would lead her to the state of Bob's experiment, as each experiment is independent. Thus Alice will not be able to deduce with certainty the result that Bob measured.

If the operators for two observables commute, the observables share a common set of eigenfunctions. If this is the case, then Alice can predict what Bob will measure.

iharuyuki said:
1. Once Bob's conducts his experiment, upon measurement, the system will collapse into one of its eigenstates which each have a probability of occurring. Since there is a certain probability of each state occurring, and each measurement could possibly result in a different eigenstate, there is no guarantee that Alice's method of deduction would lead her to the state of Bob's experiment, as each experiment is independent. Thus Alice will not be able to deduce with certainty the result that Bob measured.
Each experiment isn't independent. It's the same system. Alice measures F first, leaving it in some state, and then Bob immediately measures G.

## 1. What is the purpose of repeating measurements of observables?

The purpose of repeating measurements of observables is to ensure the accuracy and reliability of the data collected. By taking multiple measurements, any errors or inconsistencies can be identified and accounted for, resulting in more precise and trustworthy results.

## 2. How many times should measurements be repeated?

The number of times measurements should be repeated depends on the specific experiment and the level of precision required. Typically, a minimum of three repetitions is recommended, but more repetitions may be necessary for highly variable or complex systems.

## 3. How do you determine the uncertainty in repeated measurements?

The uncertainty in repeated measurements can be determined by calculating the standard deviation or the standard error of the mean. These statistical measures indicate the degree of variability or precision in the data and can help determine the reliability of the results.

## 4. What is the difference between precision and accuracy in repeated measurements?

Precision refers to how close the measurements are to each other, while accuracy refers to how close the measurements are to the true or expected value. Repeating measurements can improve precision by reducing random errors, but it does not guarantee accuracy, which can be affected by systematic errors.

## 5. How do you account for outliers in repeated measurements?

If there are outliers, or extreme values, in repeated measurements, they can be identified and removed before calculating the average or mean value. However, it is important to first investigate the cause of the outlier to determine if it is a valid data point or if it was the result of an error that should be accounted for in the analysis.

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