From my weak understanding of quantum mechanics, I want to think of the cap as the creation of a particle and it's antiparticle, and the cup as the annihilation of a particle and antiparticle.
Would the zig-zag and zag-zig equations be analogous to quantum teleportation?

Or maybe a banking analogy where the cap is the creation of a loan, with immediate equal amounts of debits and credits, the cup would then be paying off the loan, and I believe the zig-zag equation becomes something like opening one loan to pay off the current debt of another loan.