It seems to me that when we talk about entanglement, in a first-quantized kind of language we would say that the wavefunction is not separable into products of single particle wavefunctions, ie. [itex]\psi(x_1,x_2) \neq \psi_1(x_1) \psi_2(x_2)[/itex].(adsbygoogle = window.adsbygoogle || []).push({});

This would mean that any state with identical particles would be entangled... say for 1/2-spin Fermions in a singlet state, [itex]\psi_{1,2} = \tfrac{1}{\sqrt(2)} \left[ \uparrow\downarrow - \downarrow \uparrow \right][/itex] is an entangled state. So for any state, you write out a Slater determinant and you get an entangled state, right? Is this a kind of "trivial" entanglement which is not very interesting, compared to the stuff you read about in pop science articles about quantum entanglement? Is there some way to take an entangled state and measure how interesting it will be?

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# So what exactly is entanglement?

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