When does quantum entanglement cease?

Question

On Wikipedia on Quantum entanglement:

“However, this behavior gives rise to seemingly paradoxical effects: any measurement of a property of a particle performs an irreversible collapse on that particle and will change the original quantum state. In the case of entangled particles, such a measurement will be on the entangled system as a whole.”

This implies once the quantum entanglement is measured/set the entanglement ceases irreversibly.

Yet in the Quantum eraser experiment on Wikipedia:

Next, a circular polarizer is placed in front of each slit in the double-slit mask, producing clockwise circular polarization in light passing through one slit, and counter-clockwise circular polarization in the other slit. This polarization is measured at the detector, thus "marking" the photons and destroying the interference pattern

Finally, a linear polarizer is introduced in the path of the first photon of the entangled pair, giving this photon a diagonal polarization. Entanglement ensures a complementary diagonal polarization in its partner, which passes through the double-slit mask. This alters the effect of the circular polarizers

Hence, the entangled photons are measured/set two times and still retain their entanglement.

How do we reconcile these two and when does an entangled system really cease to be entangled? (assuming the photons are still moving and have not been absorbed by anything yet)

Answer 1

In the quantum eraser experiment, nothing is measured: If the which-way information would be measured, the interference would indeed be irreversibly gone.

Rather, what is happening is that the which-way information is copied to another quantum system. If that system is measured (or just ignored - which means it could still be measured), the interference pattern is indeed gone. On the other hand, if the copied information is erased (this is, un-copied), no measurement has taken place and the interference pattern is restored.

Answer 2

So in the quantum eraser experiment you essentially have 3 qubits. When you measure one of them, it is no longer entangled with the other two, but rather the results of your measurement must color your understanding of the quantum state of those other two qubits, and the results of another measurement must color your understanding of the quantum state of the last qubit.

In for example the delayed-choice quantum eraser, you have a photon's which-way information through a double-slit experiment entangled with its polarization (we rotated one slit +45 degrees and the other -45 degrees so that there is a 90-degree polarization difference between the two) but the polarization was already entangled with another polarization elsewhere: if this one is left-right then that one is up-down polarized, and vice versa. If you could really delay the choice indefinitely (like, all points are delayed until tomorrow), you could plot the distribution of the points you got, and it would look like two overlapping Gaussian bell-curves in intensity, and you would have no further information.

Then when tomorrow comes, you can choose one of two measurements to make of these other polarizations, and color those points "red" or "blue", say, if the photon goes through a piece of polaroid oriented a certain way, or not.

One of those orientations will lead to the red points being one bell curve, and the blue points being the other bell curve: in this case we would say that you "did not erase the which-way information."

Another choice of orientation will lead to two overlapping wave patterns, one of which has a maximum in the center, the other has a minimum in the center. So if you are using a coincidence counter and therefore you do not look at the blue points (say), the red points will appear to have a double-slit interference pattern. The interpretation is that you have “erased the which-way information,” because your qubit would have given you the ability to measure it but now it no longer is available to do that. But you still have the other points, too, and they describe a case where the two slits had their relative polarizations rotated by 180 degrees rather than 0. It would be hard to interpret those blue data points in quite the same way.