# Is all correlation related to quantum entanglement?

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In other words, it seems that if you have entanglement, then you have correlation (of measured properties). But is it true that if you have correlation, then you have quantum entanglement? Classically, correlation is between macro-events. But macro-events are made of micro-events. So is classical correlation the classical limit of quantum entanglement?

Thinking further, we can only measure something if there is correlation. e.g. correlation between the needle on the meter and the voltage in the circuit. Even a quantum measurement only exists if there is a correlation. For it takes an interaction to make a measurement, and we only know something about the particle being measured because it is somehow correlated with the particles interacting with it. So can you have correlation without entanglement? Isn't correlation the measure of entanglement (always)?

Thanks.

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It is easy to produce correlation without entanglement. An ordinary coin provides a good example: observations of heads on one face are strongly correlated with observations of tails on the other side.

It is easy to produce correlation without entanglement. An ordinary coin provides a good example: observations of heads on one face are strongly correlated with observations of tails on the other side.
Are you saying that the heads on one side are not entangled with the tails on the other when they are both part of the whole coin? I suppose there is no superposition. Does entanglement only exist between states that are superposed?

Nugatory
Mentor
Are you saying that the heads on one side are not entangled with the tails on the other when they are both part of the whole coin?
Yes, I am saying they are not entangled. Entanglement is a precisely defined mathematical property of the wave function, and a tossed coin doesn't have that property.
I suppose there is no superposition. Must there be superposition to get entanglement?
Yes. That's part of the definition.