There are problems that are easy to check but very hard to solve. Take a long chain of conditions, for instance, and you need to figure out whether they can all be satisfied at once. If someone hands you an answer, you can check it quickly. But finding the answer is like trying every combination on a lock: with each new condition, the work doubles.
Scientists have constructed a quantum measurement that, if it could be performed, would solve such problems very quickly. But then it would also solve problems that are considered unsolvable even for quantum computers. That is a contradiction. So no such measurement exists. It is like a key that mathematics has drawn but the physical world could not manufacture.
A strange thing follows from this: if the measurement is impossible, then certain transformations of quantum states are impossible too. And if two states cannot be transformed into each other, then their mixture and their superposition look identical. No instrument can distinguish "either one or the other" from "both at once." Such states seem to be forbidden by nature itself, not by a law of physics but by the difficulty of computation.
People used to think the quantum world turns ordinary because large objects constantly interact with their environment. Now it turns out there is another reason as well: some quantum effects simply cannot be seen, because doing so would require solving a problem that the world cannot solve quickly. The door is locked not because the lock is broken, but because the key would demand the impossible.
To undo an unwanted measurement outcome, a quantum code with four qubits is used, which encodes two logical qubits. This is the smallest possible code capable of correcting a single error with a known location.