Measuring properties of entangled photons

[sanpkl]

I am not clear on the below, so any additional information would also be good.

Let's say a pair of photons is entangled on 2 properties.

When we measure on property A -- the values for property A (for both the entangled photons) becomes determinate/locked/fixed
when we measure on property B - the values for property B (for both the entangled photons) becomes determinate/locked/fixed, however the values for property A revert to being indeterminate

Can such measurements be done without breaking the entanglement?

Has the entanglement broken and then re-created on property A?

 

[Nugatory]

When we measure on property A -- the values for property A (for both the entangled photons) becomes determinate/locked/fixed
when we measure on property B - the values for property B (for both the entangled photons) becomes determinate/locked/fixed, however the values for property A revert to being indeterminate

That's not quite how it works. After we measure property A for one particle, we know what the result of a measurement of property A on the other particle would be if it were measured. That's not the same thing as saying that property A for the other particle has become fixed/locked/determinate; if we don't measure A for the other particle, but measure B instead, then A for the other particle is not locked/fixed. (This can be and has been proven experimentally- google for "bell's theorem experiment").

With that said, you get at most one measurement on each member of the pair and then the entanglement is broken. You can measure A on both members, B on both members, or A on one and B on the other, and after that you no longer have an entangled pair.

 

[jfizzix]

Yep; even with making the measurements as general as possible there's the inescapable result that for any particular measurement outcome, the system as a result will still have to obey the uncertainty principle.

Because of this, measuring other systems correlated or entangled with the one you're interested in, or using "weak measurements" doesn't help you either.

The more you do learn about one property of a system, the less you can learn about other (non-commuting) properties of that system and vise versa.

That being said, there's nothing stopping you from learning a tiny amount about one property of a system, and then learning a lot about a complementary property.

For example, if you wanted to learn a little bit about the position distribution and a lot about the momentum distribution of a beam of photons, you can place a random screen of black and clear squares in the image plane, and then image the momentum distribution in the focal plane.

You learn a little bit about the position distribution, by narrowing down the possibilities by half, and you learn a lot about the momentum distribution by directly imaging it. At high resolution, the momentum distribution is negligibly affected, and you can just record it on a CCD camera.

The group I work with wrote a paper on it (I helped with the theory of what happens to the momentum distribution)
http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.253602
http://www.pas.rochester.edu/~jhgroup/papers/howland-prl-14-6.pdf
Yes, it's a shameless, plug, but it's a good example too of how it might be done.