Let me start out with explaining some features of quantum mechanics
that are relevant to the idea. One stunning idea is that while photons appear to travel as waveforms, they arrive at a location as discrete particles. This can be shown by the double slit experiment
which will leave your mind boggled, because a single photon will show interference with itself - it appears to sort of travel through both slits. The turning of a photon wave into a photon particle happens when the particle is measured and causes the ''collapse of the waveform
Another feature is the spooky action at a distance. The paradox is based on Quantum entanglement of two particles. Both particles have not been measured yet, but due to conservation laws, if one particle is measured, causing the collapse of the waveform, then the other particle is measured as well and will show a matching property. This effect is immediate, regardless of how far the particles are apart, which appears to contradict another important theory of physics, the Theory of Relativity, which states that nothing ever travels faster than the speed of light.
Now how is this related to fog of war? In a computer game, the fog of war is a limitation on your perception, it is knowledge that you do not have, and it especially refers to portions of the map that you cannot see.
What happens when an enemy unit moves into the fog of war is that you have to guess its position; the unit still moves according to the laws of the game, but all you know about its location is a probability distribution which will change every turn or moment passing. At some point in the game, the unit will probably reappear out of the fog of war, and you will know its location again.
Now the analogy here is that the waveform in quantum mechanics also is a probability distribution of the location of the photon, and the analogue to a measurement is what happens when an enemy unit reappears out of the fog to engage your units again.
Now I'm not implying that the world is exactly a wargame. There are other games around that work with hidden information and movement, for example the Scotland Yard board game. And clearly in quantum physics the game is more involved, since particles can exchange various properties with other particles while in the fog of war.
Finally, I want to thank everything2.com for providing these great crosslinks that save me from explaining every concept in detail.