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From what I've understood from reading different online sources including PSE*, measurements in quantum mechanics are generally argued to be irreversible (at least, when a macroscopic measuring device is used). This irreversibility is usually ascribed to an increase in total entropy (measured system $+$ measuring device) that occurs when the measurement is made. Quoting from the article "Irreversibility and Measurement in Quantum Mechanics" by Douglas M. Snyder:

Bohr (1935) maintained that quantum mechanical measurement also depended on the interaction between a macroscopic measuring instrument and the physical existent measured. He noted that when a macroscopical physical measuring apparatus is used, there is inevitably some loss of information concerning the measured system due to the resulting physical interaction. [...] For Bohr, once the information is lost in the measurement process, the measurement cannot be reversed.

However, this description only accounts for interaction-based measurements. What could we say about interaction-free measurements, then? (See the Wikipedia article for examples). If there is in those cases no physical interaction between the measuring instrument and the existent measured, by which mechanism could irreversibility be explained?

*See, for instance, this related question or this answer.

Qmechanic
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dahemar
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3 Answers3

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So imagine an electron double slit experiment where you find interference patterns build up after sending a large number of electrons through one at a time. You then set up a detector at one of the slits to detect the passing electrons. Even though this only detects about half the electrons you find no interference patterns at all build up. In a Copenhagen type interpretation the measurement of absence at that slit, despite no apparent physical event occurring in the detector, is still an interaction between the measuring device and the superposition of the electron positions that reduces this superposition to being at one slit or the other. To argue this is not an interaction is to presuppose such an interpretation is wrong, which also flies in the face of the evidence that all interference patterns disappear.

Lawrence Davies
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Realistically, a piece of lab equipment sitting idle undergoes irreversible changes from blackbody radiation, radionuclide decay, outgassing of surface atoms, etc. That probably goes double if it's powered up and "trying" to detect something.

But I think that probably isn't what Bohr had in mind when talking about undoing a measurement. What he probably had in mind was coercing the states of the world that result from different measurement outcomes into some common state, even if it isn't the state from before the measurement. In many-worlds terminology this is merging the worlds.

For that purpose, what matters is the differences between the states. There is always only one no-detection outcome (it doesn't split into "not found here" and "not found there"), and it's just as different from the detection outcomes as they are from each other, if not more different. I'd expect it to be possible to define a relative entropy of the different states and prove a relative version of the second law of thermodynamics, but I don't know anything about it.

benrg
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In quantum theory in general the outcome of an experiment depends on what happens to all of the possible states during the experiment. See Section 2 of this paper for an example:

https://arxiv.org/abs/math/9911150

You can set up an interferometer's path lengths so that photons only come out of one port. Then if a photon comes out of the other port often enough you know that one of the interferometer's arms is blocked. If you're doing single photon interference, i.e. - there is a very low probability of finding two photons in the interferometer at a time, and you block one of the arms with a detector then you would find that you don't detect a photon in that arm when you see it coming out of the wrong port. So then you have some information about the arm being blocked despite not detecting a photon there. A measurement is just an interaction that gives you some information about a system so this is a measurement of whether an arm of interferometer is blocked, albeit one in which you don't detect anything in the blocked arm.

Many real measurements such as detecting a photon at the end of an interferometer with a ccd or whatever are irreversible because information about the measured system spreads into the environment in a way that is beyond our control:

https://arxiv.org/abs/1911.06282

Interaction free measurements are irreversible in that sense because they involve a standard measurement at the end of the interferometer.

alanf
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