In principle, according to QM, information is never lost (until you make a measurement, but that's a different can of worms). In principle, in QM it is impossible to delete information. The article explains: if you burn a book, but gather detailed information about the fire and the smoke, you can reconstruct exactly what every letter on every page looked like, and every ink blot you spilled on it 10 years ago.
To quote the famous Spartan answer, If.
That is, QM predicts this is impossible. Even if you threw the book into the Sun, you would (I must emphasize again in principle) be able to measure the radiation given off by the sun and at some point identify the words of the book.
> you would (I must emphasize again in principle) be able to measure the radiation given off by the sun and at some point identify the words of the book
Does the “information” [1] survive measurements or not?
[1] “Information? Whose information? Information about what?”
My understanding is that it doesn't, but I believe that may depend on your interpretation of QM. Note also that "measurement" is pretty ill-defined.
> “Information? Whose information? Information about what?”
About the state of the system (the wavefunction). Basically in QM an isolated system cannot reach the same final state by more than one route; so, if you know what state it's in, you know exactly what route it took, what every previous state was.
Maybe the problem is more clear if moving to computation from pure physics:
In a classical computer, you can do something like "x = x & y; y = y & x". If you run this operation and find that x = 0 and y = 0, you can't know what values x and y had before, so that information was lost (ignoring other physical effects - if QM is right, the information is still retained, maybe radiated away by the processor or something).
As such, in a quantum computer, this operation simply can't be performed. Instead, you have to use an ancillary bit, z, and some QC equivalent of the Toffoli gate [0]. Then you can compute something like {x, y, z} = {x, y, z XOR (x AND y)}; {y, x, z} = {y, x, z XOR (y AND x)}; if you get the result {0, 0, 1}, you can compute exactly what values x, y and z had initially.
The same observations apply to physical interactions.
> Basically in QM an isolated system cannot reach the same final state by more than one route; so, if you know what state it's in, you know exactly what route it took, what every previous state was.
There is no way to know in what state is an isolated system - unless you know the state when you last interacted with it. You can “set” the state now and deduce the future evolution. You cannot “know” the state now and deduce the past evolution.
If you think about the whole universe, the “state” that could be described by a “wavefunction” is not a state describing the observed universe. Not even the number of elementary particles would be defined. The physical relevance is unclear.
Well, this is why I said the measurement is problematic. It's perhaps not possible even in principle to actually measure it. But, in principle, the wave-function of the sun after you throw a book that has a coffee stain into it will be different from the wave-function of the sun after you throw the same book without the coffee stain. And that difference, in turn, could be detected through measurement, as it will affect the probabilities of a measurement of the sun. Of course, this means that you will actually have to throw a whole lot of books to be able to notice this statistical difference.
> You cannot “know” the state now and deduce the past evolution.
Well, because measurement collapses the state, you are right to some extent. But on the other hand, the measurement's result will be affected by anything that has ever happened to that system in a different way.
That's different from saying that it can be measured in principle. And a having or not a coffee stain is different from the previous example. A coffee stain of a different shape would be closer.
> And that difference, in turn, could be detected through measurement, as it will affect the probabilities of a measurement of the sun.
I'm not sure how to interpret that. You just said that "It's perhaps not possible even in principle to actually measure it". [edit: maybe you mean that some kind of « statistical trace » remains, but we surely agree that’s very different from being able to identify the words in a particular book.]
Anyway, the sun is not an isolated system so it cannot be described with a wave-function. The "wave-function of the universe" - if we assume that such a thing exists which evolves unitarily since the beginning of time - would contain the "information" about the universe in which you threw a book with a coffee stain and about the universe in which you threw a stainless book and about the universes in which there is no Sun to throw things into.
Now, it's important to recognize one thing: QM is not really a linear theory, because it also has Born's rule, or the Measurement postulate. That is, while the wavefunction evolves according to purely linear equations, when you ultimately want to measure the state of the system, you get a non-linear update: the wavefunction suddenly "collapses" to a single value, and information is indeed lost (different wave-functions can collapse to the same state after a measurement). However, the measurement postulate is itself poorly understood, so its hard to introduce it into the discussion without derailing things.
There are even consistent interpretations of QM where this doesn't actually happen, such as Many Worlds, where the information is actually still preserved across the totality of the worlds.
That may be correct if the “totality of the worlds” means one single “world” described by a wave function evolving unitarily - corresponding to what you call information. This “information” cannot be destroyed but it cannot be created either. It will always be the same “information” that was already there at the beginning of time.
What is unclear is the “many worlds” part. How are they defined?
Yes, absolutely. Though it's worth noting that QM does allow for the void to have random fluctuations that are not caused by anything else, but that can interact with the existing system.
> What is unclear is the “many worlds” part. How are they defined?
There are several ways from what I've read. I personally don't think MWI really solves any problems, or that it is a good description of nature, so I haven't taken too much time to remember exactly how they do it.
The random fluctuations are random only becase we observe whether they happened or not. If you consider QM to be just the deterministic evolution of a pure quantum state there is nothing random about them. You would say that the "information" about those "random fluctuations" was always there.
> I personally don't think MWI really solves any problems
I think we agree on that.