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As I understand, an electron spin is in a superposition state until the spin is observed. Due to the observation, it will either be spin up or spin down.

Due to quantum entanglement, if one electron (electron a) is spin up the other electron (electron b), which is entangled with electron a must be spin down. Isn't this contradictory to the Schrödinger's cat thought experiment? By oberserving the spin of electron a, the spin of electron b can be determined without oberserving it.

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    $\begingroup$ "Due to quantum entanglement, if one electron (electron a) is spin up the other electron (electron b), which is entangled with electron a must be spin down." That's not true in general. Where did you read that? $\endgroup$ – DanielSank Nov 7 '19 at 15:24
  • $\begingroup$ I read an article on Sciencedaily of the topic. url: sciencedaily.com/terms/quantum_entanglement.htm $\endgroup$ – toaster_fan Nov 7 '19 at 15:30
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Schrödinger's cat thought experiment is meant to illustrate the idea of superposition, not entanglement.

Entanglement is a superposition that is shared between two different (usually thought of as spatially distant) parties. The mean different between a simple superposition is that when you talk of entanglement there are two parties that separate two parts of one shared quantum state.

You do not have this in the case of Schrödinger's cat, because in that case there is a single "observable" that is being measured (the "health state" of the cat).

Also, the statement

Due to quantum entanglement, if one electron (electron a) is spin up the other electron (electron b), which is entangled with electron a must be spin down."

is inaccurate. What is true is that two parties can share a specific type of entangled state of two spins which is such that whenever $A$ is measured to be, say, up, $B$ is measured to be down, and the other way around. The "measured" bit is essential here: you cannot say that either electron is up or down before such measurement.

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