What happens in this thought experiment?

[yuiop]

Let us say we have a type I source of entangled photons (so that we get a positive correlation if the polarising analysers are aligned). After leaving the source both photons are passed through a vertical polarising filter and continue in opposite directions. Anne is closer to the source and has a polarising analyser orientated at 45 degrees to the vertical. Bob is in the opposite direction and further away from the source than Anne. Bob's analyser is horizontally orientated. Ordinarily without entanglement, we would expect Bob to make no positive detections at his horizontal analyser, because the photons going towards him have already passed through a vertical polariser. However, since his polariser is orientated at 45 degrees relative to Anne's polariser, the entangled expectation is that Bob will get a 50% correlation with the positive detections made by Anne. The problem is that Anne could signal super-luminally to Bob by rotating her analyser. How is this situation avoided? Does placing two vertical polarisers near the source destroy the entanglement?

 

[Matterwave]

Yes to your last statement. Polarizers are "measurement devices" and therefore destroy the entaglement.

 

[yuiop]

Yes to your last statement. Polarizers are "measurement devices" and therefore destroy the entaglement.

O.K. maybe someone can help me with the terminology here. When one particle passes through a polariser, its entanglement connection to the other particle is lost, but has it de-cohered? Its vertical polarisation component has been determined (for both particles at this stage) but the horizontal component of the polarisation is still indeterminate so the photons are still (partially) in a state of superposition and the wave function has not completely collapsed at this point. Is that about right?

Now, if I may, I would like to alter the experiment slightly. Let us say we have only one vertical polariser close to the source of entangled photons on the path to Bob's detectors which are from from the source. Again, Bob's polarising detector is horizontal and he should make no detections on his side. When an entangled photon passes through the vertical polariser on Bob's side the vertical component of the photon on Anne's side is fixed, but the horizontal component is superimposed. Anne's detector polariser is orientated at 45 degrees to the vertical, so she has a 50% probability of making a positive detection on her side if a vertically polarised photon goes towards Bob. Presumably Bob still does not make any positive detections? I am trying to understand where breakdown of entanglement and breakdown of wave function/ superposition occur, but this thought experiment seems to indicate that they do not happen at the same place. Any thoughts welcome .

 

[DrChinese]

O.K. maybe someone can help me with the terminology here. When one particle passes through a polariser, its entanglement connection to the other particle is lost, but has it de-cohered? Its vertical polarisation component has been determined (for both particles at this stage) but the horizontal component of the polarisation is still indeterminate so the photons are still (partially) in a state of superposition and the wave function has not completely collapsed at this point. Is that about right?

The issue you are having relates to a small misunderstanding of photon spin components. H and V are essentially the same thing, except they are opposite. So a V polarized photon is H determinate. A 45 degree component is completely non-commuting in the sense you are considering. Both a V polarized photon and an H polarized photon are completely indeterminate at 45 degrees.