Two people read the same book, but one turns the page first and then looks at the text, while the other does the opposite. It would seem the result is the same. But in the quantum world, the order of operations changes everything.

This work examines models that output sequences of symbols, like a ticket machine. Inside such a machine, there is a hidden state that gets updated, and from it a visible symbol is extracted. Usually, the state is updated first, then the symbol is output. The authors reversed the order: output first, then update. It turns out that the two variants produce different symbol chains, and this difference can be noticed even if you wait a very long time or carefully choose the initial state.

But there is an exception. If both models are derived from the same classical model, then the order does not matter: they produce identical chains. This means the difference arises only from quantum effects, when the hidden state can be in multiple variants simultaneously. Such sensitivity to order helps reveal quantum memory that cannot be reduced to classical memory.