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I haven't seen any literature on the difference between erasing the photon's which-slit information vs just hiding it forever. Erasing quantum-information is effectively just a perpetual quarantine from the universe. A perpetual quarantine sounds hard to do though since mankind would need to exist until the very moment before the heat death to keep the information isolated. It also seems that if we fail to keep that information quarantined forever, then the photon wouldn't display an interference pattern.

So I have two questions:

Is there a difference between erasing the which-slit information, vs quarantining it forever?

And if there isn't, then would it imply that the which-slit information will leak out sometime in the future if we fail to get the photon to display the interference pattern? (scary implications!)

Thanks!

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Erasing in this context is not the same as hiding or "quarantining" information.

Thinking about this along the lines of where did the which-path information go is the wrong way to go. In quantum mechanics, the existence of some bit of information is tied to whether you are "asking" the relative question to the system. When you do something that tells you which path the photon went through you are asking the question, and it, therefore, makes sense to talk about the which-path information. However, if you instead measure in some different basis (e.g. you use a beamsplitter to make the two paths interfere and measure after it), you are not asking about which path the photon went through at all. In this case, the information is not hidden, it simply doesn't exist.

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