A question about page 6 of https://arxiv.org/pdf/quant-ph/0101077v1.pdf "The second unanswered question in the Everett picture was more subtle but equally important: what physical mechanism picks out the classical states — face up and face down for the card — as special? The problem was that from a mathematical point of view, quantum states like "face up plus face down" (let’s call this "state alpha") or "face up minus face down" ("state beta", say) are just as valid as the classical states "face up" or "face down". So just as our fallen card in state alpha can collapse into the face up or face down states, a card that is definitely face up — which equals (alpha + beta)/2 — should be able to collapse back into the alpha or beta states, or any of an infinity of other states into which "face up" can be decomposed. Why don’t we see this happen? Decoherence answered this question as well. The calculations showed that classical states could be defined and identified as simply those states that were most robust against decoherence. In other words, decoherence does more than just make off-diagonal matrix elements go away. If fact, if the alpha and beta states of our card were taken as the fundamental basis, the density matrix for our fallen card would be diagonal to start with, of the simple form density matrix = [1 0] --------------------[0 0] since the card is definitely in state alpha. However, decoherence would almost instantaneously change the state to density matrix = [1/2 0] --------------------[0 1/2] so if we could measure whether the card was in the alpha or beta-states, we would get a random outcome. In contrast, if we put the card in the state "face up", it would stay "face up" in spite of decoherence. Decoherence therefore provides what Zurek has termed a "predictability sieve", selecting out those states that display some permanence and in terms of which physics has predictive power." ------ What I'd like clarification is the following. It says above that if we could measure whether the card was in the alpha or beta-states, we would get a random outcome. Whereas if it is face-up.. it will stay face up in spite of decoherence.. Does it mean that the alpha and beta state are really still there just we don't see it because it says if you measure it you could still get random outcome?