There are two main principles at work: quantum determinism, and reversibility. Quantum determinism means that given a present wave function, its future changes are uniquely determined by the evolution operator. Reversibility refers to the fact that the evolution operator has an inverse, meaning that the past wave functions are similarly unique. With quantum determinism, reversibility, and a conserved Liouville measure, the von Neumann entropy ought to be conserved, if coarse graining is ignored.
Stephen Hawking presented rigorous theoretical arguments based on general relativity and thermodynamics which threatened to undermine these ideas about information conservation in the quantum realm. Several proposals have been put forth to resolve this paradox...."
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