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When reading about various quantum experiments the apparatus often includes things like "semitransparent mirrors", "regular mirrors", "polarization filters" and others. Usually a photon or an electron is emitted, bounces around in the device, and is measured at the other end.

And in all the experiments, all these in-between steps are considered to be "magically perfect". Nobody pays them any more attention except to mention that they're there. All mirrors reflect all photons perfectly. Polarization filters just "know" which photons to pass through and which not, etc.

But that's not how it works in real life, is it? All these parts are big, macroscopic chunks of matter with many, many atoms in them. A particle doesn't just seamlessly pass through/reflect—it bounces around in there, gets absorbed and reemitted, and entangled with God only knows how many other particles on the way.

The final particle that arrives at the detector at the end is almost certainly not the same particle that was emitted. And even if it by some miracle is, its quantum state is now hopelessly altered by all the obstacles it met on the way.

Yet nobody seems to care about this and just assumes that it's the same particle and tries to measure it and draw conclusions from that.

What am I missing here?

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    $\begingroup$ You can describe non-ideal measurements and so on. I think a canonical references is the work of Busch et al. on quantum measurements. $\endgroup$ Feb 27 at 12:16

2 Answers 2

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And in all the experiments all these in-between steps are considered to be "magically perfect". Nobody pays them any more attention except to mention that they're there. All mirrors reflect all photons perfectly. Polarization filters just "know" which photons to pass through and which not, etc.

This is true for simple textbook examples to teach undergraduates the fundamentals, but a realistic model of an experiment takes into account sources of noise from the imperfections of the apparatus.

But that's not how it works in real life, is it? All these parts are big, macroscopic chunks of matter with many, many atoms in them. A particle doesn't just seamlessly pass through/reflect - it bounces around in there, gets absorbed and re-emitted, and entangled with god only knows how many other particles on the way.

Yes, this is true. This is handled with the theory of "open quantum systems". In the case of modelling discrete elements such as mirrors, etc., usually it suffices to go beyond unitary transformations acting on pure states, and generalise to Kraus operators acting on density matrices.

In general, if we're dealing with continual sources of noise, interactions with the heat bath causing the noise usually happen over such a short time scale that you can model it as instantaneous and memoryless, in which case you get Lindblad master equations and related/equivalent methods such as quantum trajectory theory. In the case when these approximations don't hold, this requires more explicit modelling of the particle/heat bath interaction and is usually a matter of active research.

A good general reference is Quantum Noise by Gardiner and Zoller, as well as Gardiner and Collet's original paper on quantum input/output relations.

The final particle that arrives at the detector at the end is almost certainly not the same particle that was emitted. And even if it by some miracle is, its quantum state is now hopelessly altered by all the obstacles it met on the way.

Fundamental quantum particles are indistinguishable. The effect on particles with distinguishable internal states such as atoms can simply be modelled by the previously mentioned Lindblad equations or Kraus operators causing transitions between internal states. The possibility of particle loss is handled by using a second quantised description.

Yet nobody seems to care about this and just assumes that it's the same particle and tries to measure it and draw conclusions from that.

I wouldn't say nobody cares. Pretty much every experimentalist these days takes the effects of noise into account.

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    $\begingroup$ I would suggest that there is a hard-fought chapter called "somebody cares" in most PhD theses on quantum information. $\endgroup$
    – rob
    Feb 29 at 0:33
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    $\begingroup$ "quantum particles are indistinguishable" but in an experiment involving entanglement between two particles, don't we care about those specific particles vs others of the same class? $\endgroup$
    – user4574
    Feb 29 at 19:40
  • $\begingroup$ When a photon goes into a mirror and another photon comes out, the outgoing photon will typically "inherit" most of the properties of the incoming photon, including entanglement. The important question for analysis is, to what extent does the operation preserve the properties you want. There is no additional fact of the matter as to whether it is the "same photon"; a photon has no identity other than the bundle of properties making up its quantum state. $\endgroup$ Mar 1 at 1:03
  • $\begingroup$ (Technically entanglement is not a property of the photon's state; it is a joint property of the photon and whatever it's entangled with. However it works the same way; the outgoing photon will be entangled more or less the same way as the incoming photon. So it's effectively the "same photon". It will lose a little to the interaction with the mirror; that will translate to a small probability of getting an unexpected outcome, but you just need to keep the probability small enough that you can deal with it.) $\endgroup$ Mar 1 at 1:07
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Without disputing anything said in AwkwardWhale's correct answer, and focusing on photon behavior specifically (but the same basic theory applies to any quantum system):

In modern optics, we have tools that are extremely precise and can probe all the things you mention in great detail. Specifically: a) we have the theory of Fock states (where photon number is precisely known; and b) sources of entangled photon pair (N=2).

Were any of the items you mention a significant factor, it would show up immediately in Bell tests. This is because "noise", "environmental decoherence", and other things would terminate the entanglement. In that case, the entanglement would end and the Bell (CHSH) inequality would not be violated. That doesn't happen.

Instead, entanglement has been demonstrated with very high precision through filters, beam splitters, mirrors, fiber, wave plates and so forth with negligible effect. This has been accomplished over very large distances, from 10 km up to over 100 km. The only thing that has been shown to make much difference is when entangled photons travel through the atmosphere.

So you can see from these situations, such optical gear makes virtually no impact at all. Here is a basic example:

Violation of Bell inequalities by photons more than 10 km apart (1998)

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    $\begingroup$ Isn't it weird though? I would think that any and all interactions that a photon might have with optical devices would immediately destroy any quantum state that it had. $\endgroup$
    – Vilx-
    Feb 27 at 18:09
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    $\begingroup$ It goes back to theory really. The transformations alter certain characteristics of the photon in very specific ways. And that does not otherwise end the entanglement. Note that technically, an entangled photon pair is a system of exactly 2 photons. Sometimes such a system is referred to as a "biphoton" to indicate as such. They can remain in that combined state for a substantial period of time/space. $\endgroup$
    – DrChinese
    Feb 27 at 20:31

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