Can Quantum Measurement Be Detected After The Fact? My question is simple and has a crude drawing associated with it. I was watching some videos of the quantum erasure experiments and being a computer scientist have researched quantum encryption (Something already in use) which is used to detect whether or not a MITM (Man in the middle) attack has occurred, giving two parties knowledge that their conversation hasn't been eavesdropped upon.
In the thought experiment (That has been carried out) where an astronomer on Earth is observing photons from a distant star where a galaxy lies in between causing lensing, would it be possible to detect whether or not those photons had already been observed somewhere between the star and the galaxy? Would that be possible by detecting a clump pattern where an interference pattern should be observed? Or am I not thinking it through properly? The implications would of course be some form of quantum communication across vast space and time.
Another question could be: Could the observer near "Alien Planet" detect if/how we've observed the photons to produce some form of communication/known existence?

 A: No, you can't tell if someone else has observed an entangled copy of your quantum information. And the YouTube videos about the delayed choice experiment are particularly bad, even for quantum things.
You can get evidence that an entangled copy was made, because your qubit's density matrix will correspond to a mixed state instead of a pure state (center of Bloch sphere vs surface of Bloch sphere). But you can't use your qubit to learn anything about what was done to the entangled copy.
I talked about this in a blog post about delayed erasure, though you might prefer an actual paper on the subject. Here's the relevant diagram from the post:

Without waiting to compare notes with the alien, so you can condition on their results (that's the "filtering" in the diagram), you'll see the same thing regardless of what they've done or will do. And this isn't just an inference based on no one finding a way to do communication-with-just-entanglement yet, there's a mathematical theorem about it.
A: The simple answer is "No more than with classical communication" and that is the only correct answer. Having said that... there is an interesting application for your scenario and that's the question if such a system can show multi-path interference between a beam going around one side of the galaxy and another beam going around the other. I would like to see that observation and data analysis. 
