Nonlocality & the measurement problem.

[misogynisticfeminist]

I've got a few questions here, is the non-local "communication" between 2 entangled particles instantaneous, or is it just simply faster than the speed of light? Is this communication simply part of their common wavefunction or is it somehow a physical signal which somehow travels faster than light, no matter what special relativity may say?

And also, another unrelated question, if I open the porthole in an interferometer but do not look into it, or do any "measurements" on it, does it still constitute a measurement, collapsing the wavefunction?

 

[marlon]

Well let's say that Alice and Bob both deliver a particle (A and B) and that we get an entangled state. Many copies of that state are prepared and Alice takes all A qubits to Pluto and Bob takes all B qubits and stays here on earth. If Bob wants to send a one-bit message to Alice he chooses to measure either the spin along the X or Z axis. Now in order to read the ensemble , Alice IMMEDIATELY measures her spins to see which ensemble has been prepared.

Now, you could say that there must be faster then light communication, but there is one little fact that says this is NOT the case. The ensemble of both Bob and Alice (i mean the two results they each get when having measured the spin along the X and Z-axis) are described by the same density matrix. So basically, this means that there is no measurement that Alice can perform in order to distinguish the two ensembles (spin up and down along the X or Z axis) and thus concluding what action Bob performed. The message is unreadable.



Suppose Bob has spin UP, UP for the two measurements (along X and Z axis)
Then due to the entanglement, Alice will have also UP, UP in X and Z direction. Now Alice performs the measurement in order to determen which direction the first qubit is aligned to. She has a 50/50 chance it is X or Z. Just the same for the second qubit. Thus the message is unreadable. She doens't know anything new here...

regards
marlon

 

[marlon]

And also, another unrelated question, if I open the porthole in an interferometer but do not look into it, or do any "measurements" on it, does it still constitute a measurement, collapsing the wavefunction?

Aren't you referring to the Welcher-Weg-experiment. This is German for Which Way, or the quantum eraser.

For example suppose we let a bundel of particle pass through an apparatus that measures the spin in the Z-direction. In this situation there is entanglement of the spins A and this yields the measurement-situation. I mean that via the entanglement between spin A and B (just like in the previous post), we know that for example the outcome 0 means spin down along the Z-axis and 1 means spin up along the Z-axis. The coherence of the two spin-postions of spin A along the Z-axis is lost because we can find out there position by observing spin B.

Yet, if we measure the spin B along the X-axis then the info about whether spin A is up or down along the Z-axis, is GONE ! This is because Bob (spin B) did not retain the "which-way" information that he could have obtained by looking at the outcome when the bundle passed the apparatus that measured the spin along the Z-axis.

To be clear I state that first the bundle passed through the apparatus that measures the spin along the Z-axis. We get two bundles (UP, DOWN) then we do nothing and let the two bundles converge to one and this bundel is passed through an analoguous machine that measures the spins along the X-axis.


Also, keep in mind that a spin along the z-axis (both up and down) can be written as a superposition of the spin up and spin down along the X-axis. The same goes for a spin in the X-direction written as a superposition of spin up and down along the z-axis.
regards
marlon