I seems strange to me that I could not easily find information on "when quantum entanglement ends?", "What causes quantum entanglement to end?". Google search finds explanations of what quantum entanglement is, wiki article gives a lot of info, definition of entanglement:

Quantum entanglement is a physical phenomenon that occurs when a pair or group of particles are generated, interact, or share spatial proximity in a way such that the quantum state of each particle of the pair or group cannot be described independently of the state of the others

ways to create one, which I found very informative to myself. I doubt entanglement is forever, in fact I recall vaguely it ends e.g. with measurement, but strangely now could not find any place where it is stated that clearly.

That question here When does quantum entanglement cease? also states:

This implies once the quantum entanglement is measured/set the entanglement ceases irreversibly.

And in answers I did not see arguments against that part. But no objections there IMHO does not mean automatically it is correct as other reason for OP misconception was presented.

Could somebody list all ways in which entanglement ends?


1 Answer 1


The most popular approaches to quantum mechanics would argue that the entanglements never end, they just get arbitrarily weak. In theories built on decoherence, the entanglements are always present, but they become less and less statistically important as they interact with a "heat bath" of particles in a random state. When they do so, the effect of these random interactions start to overpower the effect of the entanglement and the entanglement becomes increasingly negligible for predicting future measurements. When the entanglement accounts for 0.00000000000001% of the expected result of a measurement, the effect of this entanglement falls into the noise in our measurement errors and we can hand-wave it away.

What complicates this somewhat is that the major interpretations of quantum mechanics claim that a "measurement" causes this decoherence. This is because the purpose of the interpretations of quantum mechanics is to tie the world of quantum mechanics to a hypothetical world governed by classical mechanics. This connection is done through vague terms like "measurement" and "collapse."

What we find is that, in practice, the things called "measurements" can be implemented by thinking about them with the decoherence model. In a sense, we can use this way of thinking to realize the very abstract concepts of "measurement." They are typically built around using a great body of atoms in a known state (put there with energy in the classical sense), which then interact with a quantum system in a way such that the statistical expectation of the results looks like a measurement in the classical sense (like how one might measure a stick to be 12 cm long). These "measurements" do indeed have the effect of breaking entanglements in the way you describe, and the exact process of doing so is well described by multiple interactions with particles that are in a random state.

Something I found useful for working through this is the idea of weak measurements. While the exact meaning of a weak measurement is not universally agreed upon, it typically takes the form of doing an interaction with the system that falls short of being a "measurement," in effect creating an entanglement, and then taking the actual measurement later. Seeing how a weak measurement of an entangled system causes entanglements of its own is very helpful for seeing how these entanglements and measurements pile up.

  • $\begingroup$ Thank you. I hope I will study decoherence in more detail. For clear example, is it possible to say how much of entanglement "goes away" from expected result from one interaction with one particle in a random state? $\endgroup$ Nov 20, 2020 at 4:54
  • $\begingroup$ Also, as a side note, I would like to hear your thoughts about the definition from wiki, which I added to the question. I mean would definition be better made using term of "coherence" directly, not as now wiki article uses "coherence" later to explain entanglement? $\endgroup$ Nov 20, 2020 at 5:02
  • $\begingroup$ @Martian2020 The answer to your first question is yes. It is possible to say how much goes away. If you can write down the operator for the interaction and a random variable describing the state of the external particle doing the interacting, you can come up with an exact answer using math. However, for "interactions in general," one cannot say how fast it goes away, just as how one cannot say how heavy an object is without knowing which object one is speaking of. $\endgroup$
    – Cort Ammon
    Nov 20, 2020 at 5:05
  • $\begingroup$ @Martian2020 My personal thoughts would be that all systems are well described using quantum mechanics (other than gravity, which is an entirely separate topic). Most systems are well described using classical mechanics. However, there are some systems which have properties which are predicted in QM and not predicted in classical mechanics, and they tend to be characterized by an informal sense of "moving together," hence coherence. Decoherence occurs when one does things that cause the particles to cease to "move together" in an informal sense. $\endgroup$
    – Cort Ammon
    Nov 20, 2020 at 5:07
  • $\begingroup$ I think the key behavior that we see in "coherence" is two particles that, according to classical mechanics, should be completely independent, such that measuring one says nothing about what would happen if you measured the other. But, in these systems, find a peculiarity that measurements about one particle do indeed say something about measurements that may be undertaken on the other. If you think in QM terms, the situation is quite literally nothing special, but in classical terms, its perplexing, so we have terms to describe it. $\endgroup$
    – Cort Ammon
    Nov 20, 2020 at 5:09

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