I watched a video featuring Leonard Susskind in which he took a small bowl of water and added three drops of food coloring. He swirled it around. At first you could tell where the drops must have entered the water, but after a while you could not tell anymore. He said that a cornerstone of physics is that information cannot ever be destroyed and that the information is always there -- we just cannot see it.
I see two issues here and I'm hoping for some clarification.
The particles can never be traced back to their origin. The uncertainty principle says that other particles have popped in and out of existence. These may have interfered with the particles in the water and cannot be traced back. So information is in fact lost.
Let's take the same type of experiment but narrow the scope. Instead of this, I put four protons into some sort of container that can hold them. Not sure what that is or if it's more of a field, but for this thought experiment, let's just say I have a box with four particles in it. At first you know where they originated by watching them (if you could watch them). But after a long enough time, the particles will occupy the same position and spin state that they did at some point in the past. So the first time they occupied this state they trace back to your initial placement. The second time they hit this state they trace back to the first state. So you cannot actually trace them back to see where they originated in the container.
Perhaps the second thought experiment has some flaws in it but I'm hoping you can see what I'm getting at. That a duplicated state must mean that the originating positions and information is lost, and given enough time you'll always get a duplicated state.
