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If I have understood correctly, in time a single qubit in superposition will collapse on it's own to the $|0\rangle$ or $|1\rangle$ state, but I thought it only collapsed when measured. How is the collapse explained if there isn't any measurement?

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    $\begingroup$ The qubit is entangled with the environment, and the information leaks into the environment. Since we do not control the environment, the information is lost. You can read Chapter 3 of Preskill's lectures for details. theory.caltech.edu/~preskill/ph229 $\endgroup$
    – EvgeniyZh
    Sep 6, 2023 at 10:30
  • $\begingroup$ Imagine for example that the qubit is a particle being kept in a vacuum, but not a perfect vacuum. Then it will be "measured" at a very low rate by the occasional interactions with gas molecules, even if we don't measure it on purpose. (I think in reality we can pull a good enough vacuum that other factors will decohere it first, but this happens to be an easy example to visualize.) $\endgroup$ Sep 6, 2023 at 18:05
  • $\begingroup$ In a trapped ion quantum computer, the ion which is in a superposition state is kept in an electric field under vacuum. The claim is that the decoherence time is long (about 50 seconds) as the ion is kept in vacuum and has little chance of interacting with the environment. But I wonder, doesn't interaction with the electric field constitute a "measurement" and lead to decoherence? $\endgroup$
    – Max
    Sep 6, 2023 at 21:52
  • $\begingroup$ This is a fundamental question in quantum theory, the interpretation of quantum wave function with respect to collapse/measurement: There are several different interpretations: en.wikipedia.org/wiki/… for a summary. $\endgroup$ Sep 7, 2023 at 0:24

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When we measure a qubit in superposition, we interact with the system, causing it to collapse into either $|0\rangle$ or $|1\rangle$, with certain probabilities determined by the coefficients in the superposition.

If a qubit were perfectly isolated, it would remain in a superposition indefinitely (or until a measurement, but then it wouldn't be isolated anymore!). However, qubits interact and become entangled (as per @EvgeniyZh) with their environment, which can cause a collapse of superposition and the transition to classical behavior (which is very well explained here). This is decoherence. Decoherence is an issue in quantum computing because, if a qubit becomes entangled with the environment and decoheres, we can’t undo the damage to the qubit if we don’t have full knowledge of the environment in which it was entangled with (which we don't).

So in essence, decoherence leads to the leakage of quantum information into the surrounding environment, and since we lack the ability to control this environment, the retrieval of this information becomes impossible.

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