Consecutive Measurements on One of an Entangled Pair

[Q-reeus]

I'd like some informed opinion on the following scenario, which in a certain article forms the basis of a controversial claim.
Suppose an entangled spin anti-correlated pair of particles are generated by some process. Particle A flies off along the +z direction, particle B along the -z direction. In particle A's path are placed three consecutively spaced spin detectors. The first measures say along the x axis, the second along the y axis, the third along the x-axis again. We can choose to measure particle B's spin either after the first, second, or third measurement performed on particle A. Is it the case that entanglement ceases after the first measurement on A, in which case particle B's spin will always be measured as the opposite of the first x-axis measurement on A, regardless of subsequent measurements on A. Or does entanglement survive until particle B is actually measured, in which case presumably it could have the anti-correlated value of particle A's second or third measurement, depending on just when measurement on B is performed?

 

[DrChinese]

There is "some" sense in which the A's entangled state survives after A's first measurement. But probably not in the fashion you might guess.

1. If you measure A's x spin first, then A is no longer spin entangled with B. It does not really matter whether A or B is measured first, the results are identical and cannot be distinguished.

2. If you measure A's x spin first, it is *possible* that A may remain position/momentum entangled with B thereafter. This is because spin commutes with p/q.

 

[Q-reeus]

There is "some" sense in which the A's entangled state survives after A's first measurement. But probably not in the fashion you might guess.

1. If you measure A's x spin first, then A is no longer spin entangled with B. It does not really matter whether A or B is measured first, the results are identical and cannot be distinguished.

2. If you measure A's x spin first, it is *possible* that A may remain position/momentum entangled with B thereafter. This is because spin commutes with p/q.

Thanks DrC. Point 1 answers my main query, falsifying the claim in the article I alluded to, which was that subsequent measurements on A could potentially force changes in the definite spin state of particle B remotely. Point 2 I am less clear on. So in general there will be jointly spin and position/momentum anti-correlation initially? Could you explain how spin commutes with p/q? I naively assumed they are unlinked quantities.