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Let say we have the state $ |\varphi⟩ = \alpha|0⟩ + \beta|1⟩ $

Measuring this state provoke a change, $\epsilon$ to the system, $S$, making the state of $|\varphi⟩$ collapse to either $|0⟩$ or $|1⟩$.

The laws of physics, as far as I know, are always stated as being reversible, meaning that no information is lost.

From that and the second postuale of quantum mechanic, wouldn't that mean, that if we are able to measure, or more likely to estimate precisely, the impact of $\epsilon$ on $S$, we should, theoretically, be able to know the actual state $|\varphi⟩$ before collapse?

And if yes, is it something that is pursued by researcher or why not?

Thanks for your help

TSS22
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1 Answers1

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In interpretations of quantum mechanics such as the Copenhagen interpretation, wave function collapse is not reversible. Wave function collapse does indeed result in a loss of information as far as the observer/measuring apparatus is concerned. Or, at least, there is a dissipation of information into the wider environment in such a way that it cannot be recovered.

In other interpretations such as the many-worlds interpretation, information is not lost because the wave function never collapses. In principle the original state could be recovered by observing the frequencies of different outcomes across all possible branching worlds - but in practice we cannot do this because our post-collapse knowledge is limited to one branch.

gandalf61
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  • It seems like a cruel joke to say that something isn't lost if it has gone to someplace where you can never find it :-) – D. Halsey Mar 21 '23 at 18:14
  • I am not thinking of making it reversible, but just to recompute the $\alpha$ and $\beta$ factor. But as mentioned in one of the answer in the post my answer was associated, it seems doable, as the example with the interferometer (if I interpreted it correctly), and of course if we work on closed system. Thanks for your help! – TSS22 Mar 24 '23 at 20:24