Why Quantum Information is Never Destroyed | Space Time

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Conservation of information?! I'm a bit shocked PBS would put it that way. The idea sounds like it's tightly bound to a handful of interpretations and there are at least a few theories that either partially or even fully negate this idea. Still, I never thought I'd hear the words 'conservation of information' coming out of Matt O'Dowd, sounds a bit... Chopraesque of them.

"Conservation of information" means that the wave function at any one moment in time could be reconstructed in principle from the wave function at any other moment in time, and is a trivial logical consequence of unitarity. As some interpretations (like Many Worlds theory) reject any non-unitary time evolution of the wave function (namely, wave function collapse), "conservation of information" would be a fundamental part of those interpretations.

Yeah, that's pretty much exactly how they explained it in the video - that with the models under consideration a given state could not/would not be arrived at from multiple prior states. A person has to perhaps understand as well that they don't mean approximate states, the way we'd typically think of water for example being able to hit any side of a funnel and go down the center and out the bottom, but rather exact particle-per-particle placement and motion across time.