atyy said:
Do you disagree with this statement: "Before Alice's measurement the state is |hh⟩+|vv⟩|hh⟩+|vv⟩|hh \rangle + |vv \rangle, and after the measurement the state collapses to |hh⟩|hh⟩|hh \rangle if Alice measures her photon to be horizontal"?
vanhees71 said:
Yes, I disagree with this statement. Correct is: If A's photon passes the h-polarization filter she associates the state hh⟩hh⟩hh \rangle to the two photons. However, her measurement has no instantaneous influence on B's photon, i.e., there must not be a collapse if the interpretation should be consistent with the very construction of QED as a local relativistic QFT, and you don't need it!
Would I be right in thinking that the source of the disagreement here is in that troublesome word 'collapse'?
Let's consider an entanglement-swapping scenario in which Alice has spin-1/2 particles (1,2) prepared in a maximally entangled state, and Bob has spin-1/2 particles (3,4) also prepared in a maximally entangled state. So one thing we can say for definite is that particles (1,4) are not entangled.
Alice sends particle 2 to Clive and Bob sends particle 3 to Clive.
Clive makes a Bell measurement on particles (2,3).
There is no doubt whatsoever that whether we think about it in terms of 'collapse' or not that after the Bell measurement of Clive, the particles (1,4) are now entangled - at least that would be the traditional view based on the axioms.
Of course, without the supplementary information about Clive's actual measurement result, Alice and Bob can't do much with this since (without this supplementary information) they would have to assign a mixture of Bell states to their particles (1,4).
But aren't we justified in saying that (1,4) are really entangled - even though we might not know which particular entangled state we have (without further information about Clive's result)? The knowledge of Clive's result doesn't really alter the fact that the particles (1,4)
are entangled now - it just allows us to assign a specific entangled state. It's very tempting to make a statement, based on this, that the particles (1,4) are now actually
in a particular entangled quantum state.
In other words there is a definite physical difference in particles (1,4) before and after Clive's measurement (before : no entanglement, after : entanglement)
So we could describe Clive's measurement as effecting a 'collapse' onto a particular entangled state - even though this way of thinking is at odds with the explicitly local construction of QFT - and,
as far as the prediction of subsequent experimental results is concerned, there would be no inconsistency or error in so doing.
Let's go one step further and suppose that Clive sends the information about his result on to Alice and Bob. When they receive this update - they can now assign a more appropriate state (a specific pure entangled state). So as soon as they receive this information their state assignation has 'collapsed' from mixed to pure - but nothing has changed, only their knowledge.
But, isn't this whole disagreement about 'collapse' and what it means all a bit academic? There are no predicted incorrect experimental consequences (as far as I'm aware) from adopting a traditional 'collapse' picture - just as there are no predicted incorrect experimental consequences from rejecting this view and doing things without explicitly thinking of collapse in this fashion.