Quantum mechanics comes with a list of allowed operations, and until recently it was assumed that any operation on that list would sooner or later find its way into a laboratory. It turns out that this is not so. Some measurements are like a door for which mathematics has issued a key, but the physical world refuses to cut it.
The key to this door is a problem computer scientists call "3SAT." It is like a puzzle where you have to assign truth and falsehood along a long chain of conditions so that all of them hold at once. Checking a finished solution is easy, but finding one takes agonizingly long if there are many conditions. The authors of the paper constructed a clever quantum measurement that, if it could be performed, would knock off such puzzles one after another. And that is where things get really interesting.
If such a measurement existed, it would solve problems that even a quantum computer, by general consensus, cannot handle in any reasonable time. So this measurement does not exist. Not "has not been invented yet," but does not exist in principle, just as there is no key to a door that leads nowhere. Such measurements have been dubbed unobservable.
Strange consequences grow from this simple conclusion. If a measurement cannot be performed, then the transformation of a quantum state that corresponds to it is impossible as well. Which means there exist pairs of states that no allowed evolution can turn into each other. Worse still: a superposition of such states, with the system in both at once, is indistinguishable from a plain mixture in which the system is in one or the other. No instrument will see the difference.
This resembles a rule physicists call superselection: certain combinations of states are simply forbidden. Usually the ban is explained by conservation laws or by interaction with the environment. Here, though, the ban grows out of computational complexity. The door is locked not because the lock is broken, but because the key would require solving a problem the world cannot solve quickly.
Until now it was thought that the quantum world turns classical because large systems continuously exchange information with their environment, a process known as decoherence. The new work adds a second, independent source: even with no environment at all, some quantum effects remain unobservable simply because observing them would require computations beyond the possible. The classical world, perhaps, is not so much born as left over, the only thing visible from behind a locked door.
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.