Repeating measurement of observables?

[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.

 

[vela]

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?

 

[iharuyuki]

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.

 

[DCN]

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.

 

[vela]

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.