# Does information get lost by measurement?

• I
Gold Member

## Main Question or Discussion Point

If we consider quantum wavefunction-collapse, when we end up in a world-thread with a specific value of the measurement outcome, has information got lost?

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Demystifier
It depends on what do you mean by "information". Information about what? If you mean information about the state before the measurement, then yes, it gets lost.

Gold Member
It depends on what do you mean by "information". Information about what?
Yes, I was wondering about that...

I was imagining that when an oucome has manifested, information about the other outcomes that were possible is lost? Like in MWI, each world-thread contains a single outcome, and all possible outcomes have gone isolating from each other.
If you mean information about the state before the measurement, then yes, it gets lost.
Ok. So I mean is that the only information that gets lost? And is that a problem? Does the new state compensate for the loss of the old state?

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Demystifier
I was imagining that when an oucome has manifested, information about the other outcomes that were possible is lost?
Yes.

Ok. So I mean is that the only information that gets lost?
Yes.

And is that a problem?
Not really. (But the idea of collapse is problematic for other reasons that have nothing to do with information loss.)

Does the new state compensate for the loss of the old state?
Yes. In a sense, the new state contains the same "amount" of information.

kith
This question is quite subtle because a) it is linked to the measurement problem and b) information is a subtle concept, especially in QM.

If we try to model the measuring process, the system of interest gets entangled with the measurement apparatus during the process. The state of system+apparatus remains a state of maximum information$^*$ (a so-called pure state) throughout the whole process. But it is a very peculiar property of quantum systems, that a maximum information state of the whole system doesn't necessarily imply a maximum information state of its parts and indeed the state of the system alone is not a state of maximum information if the system and apparatus are entangled.

But that's not the whole story. When the measurement is completed, the observer has obtained a definite result which corresponds again to a state of maximum knowledge for the system alone. The modelling doesn't yield this which is essentially the measurement problem. If you want to say definite things about this second step, you need to invoke an interpretation.

In any case: the thing about the measurement process from an information theoretic perspective is that it contains a combination of decreasing and increasing information. The initial and the final state are both states of maximum information.

This might seem odd, because the very idea of measurement is to acquire information. But the concept of information in QM is more subtle than in classical mechanics where we don't have incompatible pieces of information. If, for example, the system is spatially confined to a high degree before a highly accurate momentum measurement, it won't have this property after the measurement.

$^*$ or to put it more technically: of zero entropy

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Hmmm.... The before-measurement state is what's prepared by the experimenter, his macroscopic actions, right? So all the information is classical , it can hardly be lost.

EPR
Gold Member
How can a quantum state be 'classical' before measurement?!

Hi all,

Concerning the collapse of the wavefunction, Franck Laloë proposes a theoretical model : https://phys.org/news/2020-02-deconstructing-schrdinger-cat.html

The preprint : https://arxiv.org/abs/1905.12047

One approach to solving this problem involves adding a small, random extra term to the Schrödinger equation, which allows the quantum state vector to 'collapse,' ensuring that—as is observed in the macroscopic universe—the outcome of each measurement is unique. Laloë's theory combines this interpretation with another from de Broglie and Bohm and relates the origins of the quantum collapse to the universal gravitational field. This approach can be applied equally to all objects, quantum and macroscopic: that is, to cats as much as to atoms.

In contrast with the usual interpretations of the de Broglie-Bohm (dBB) theory, we make no particular assumption concerning the physical reality of these positions; they can be seen, either as physically real, or as a pure mathematical object appearing in the dynamical equations.
Patrick