I would like to understand this image, of a "payload preparation" gate. A single H gate will create a superposition, while the phase will rotate 45 degrees. What does the second H gate do in this commonly used subcircuit?

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"Payload preperation gate" is just a fancy name for preparing the message with a more clear setting with the probability of 85.4% ∣0⟩ and 14.6% ∣1⟩ in this case. The chance of being a zero is less than that of one. A standard example of teleportation gives a 50% chance, in that case it is not a clear 0 or 1. The second H gate changes the relative phase of Alice between the 0 and 1 bit. Without the H gate it is 45 and with H gate it is 90 degrees. It does not really matter what sort of message you will give, it depends on what you want to show. Quantum teleporation with a payload

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