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Is a highly entangled quantum system synonymous with a strongly correlated system?

From wikipedia a key characteristic of a strongly correlated system is that "the behavior of their electrons or spinons cannot be described effectively in terms of non-interacting entities"

For a highly entangled system we have the following definition: "each particle of the group cannot be described independently of the state of the others"

To me, these sound the same and I was wondering if there is some nuance I am missing. The reason I ask is because I have seen people list their research interests as "highly entangled systems and strongly correlated systems" which leads me to believe that there is a fundamental difference between the two.

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    $\begingroup$ You can have strongly correlated systems which aren't entangled, for instance in statistical mechanics. $\endgroup$
    – r_phys
    Commented Mar 21, 2022 at 19:19

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Entanglement can be thought of as something that causes the state to produce "stronger than classical" correlations. Understanding what precisely this means can be tricky, but at least for pure entangled states, this statement can be substantiated for example by the fact that these states all violate some Bell inequality, meaning they produce correlations (when suitably measured) which cannot be explained classically (more precisely, with local realistic probability distribution).

For example, a separable (i.e. non-entangled) state such as $\sum_k |k\rangle\!\langle k|\otimes |k\rangle\!\langle k|$ corresponds to a classical state in which the two parties are maximally correlated. On the other hand, the pure (maximally) entangled state $\sum_k |kk\rangle$ will give the same exact correlations as the other one, when measured in the computational basis, but at the same time will give correlated results even when different measurement bases are used. This does not happen (as much) for the separable correlated state above, which is why one can say that entanglement is sort of a form of stronger correlation.

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I think what you need is to make the difference between entanglement and correlation.

If two particles are entangled, then knowing the state of one (say the spin) would automatically give you the state of the other one.

Correlation on the other hand will only give you additional information about the other particle but not necessarily all the information.

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    $\begingroup$ The typical meaning of 'entanglement' denotes the presence of some quantum correlations. This does not necessarily mean 'full entanglement'. For example, if knowing the spin of one particle will give you the state of the other one with 60% accuracy, it is still considered entanglement $\endgroup$
    – Wouter
    Commented Mar 23, 2022 at 3:34

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