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In quantum mechanics, for two observables to be compatible, successive measurements of the observables, say A$A$ and B$B$, should yield the same result as earlier, i.e if we do the measurements with the order $A \to B \to A$, the result from the first A$A$ and the last A$A$ should be the same, and similarly, for $B \to A \to B$.

However, is it possible for two observables to have the following relation;

If we measure $A \to B \to A$, the first and the last measurement of $A$ yield the same result, but if we measure $B\to A \to B$, the first and the last measurement of $B$ yields different measurements (in general).

In quantum mechanics, for two observables to be compatible, successive measurements of the observables, say A and B, should yield the same result as earlier, i.e if we do the measurements with the order $A \to B \to A$, the result from the first A and the last A should be the same, and similarly, for $B \to A \to B$.

However, is it possible for two observables to have the following relation;

If we measure $A \to B \to A$, the first and the last measurement of $A$ yield the same result, but if we measure $B\to A \to B$, the first and the last measurement of $B$ yields different measurements (in general).

In quantum mechanics, for two observables to be compatible, successive measurements of the observables, say $A$ and $B$, should yield the same result as earlier, i.e if we do the measurements with the order $A \to B \to A$, the result from the first $A$ and the last $A$ should be the same, and similarly, for $B \to A \to B$.

However, is it possible for two observables to have the following relation;

If we measure $A \to B \to A$, the first and the last measurement of $A$ yield the same result, but if we measure $B\to A \to B$, the first and the last measurement of $B$ yields different measurements (in general).

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Is is possible to have a pair commuting observables only in a single direction?

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In quantum mechanics, for two observables to be compatible, successive measurements of the observables, say A and B, should yield the same result as earlier, i.e if we do the measurements with the order $A -> B -> A$$A \to B \to A$, the result from the first A and the last A should be the same, and similarly, for $B -> A -> B$$B \to A \to B$.

However, is it possible for two observables to have the following relation;

If we measure $A-> B -> A$$A \to B \to A$, the first and the last measurement of $A$ yield the same result, but if we measure $B-> A -> B$$B\to A \to B$, the first and the last measurement of $B$ yields different measurements (in general).

In quantum mechanics, for two observables to be compatible, successive measurements of the observables, say A and B, should yield the same result as earlier, i.e if we do the measurements with the order $A -> B -> A$, the result from the first A and the last A should be the same, and similarly, for $B -> A -> B$.

However, is it possible for two observables to have the following relation;

If we measure $A-> B -> A$, the first and the last measurement of $A$ yield the same result, but if we measure $B-> A -> B$, the first and the last measurement of $B$ yields different measurements (in general).

In quantum mechanics, for two observables to be compatible, successive measurements of the observables, say A and B, should yield the same result as earlier, i.e if we do the measurements with the order $A \to B \to A$, the result from the first A and the last A should be the same, and similarly, for $B \to A \to B$.

However, is it possible for two observables to have the following relation;

If we measure $A \to B \to A$, the first and the last measurement of $A$ yield the same result, but if we measure $B\to A \to B$, the first and the last measurement of $B$ yields different measurements (in general).

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