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I'm struggling to find any information on how to check if a pair of particles are entangled.

I've found lots of information on how to entangle particles, but I'm wondering how to check entanglement on any given pair of particles, since any measurement of the quantum system will collapse the system to the state which was the result of the measurement.

The only way I can think of is measuring one particle and then by the definition/concept of entanglement you will know the result of a measurement of the other particle if they are entangled. Is this the only way to know if a pair of particles are entangled?

Any help is appreciated! Thanks!

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  • $\begingroup$ Make an observation all of whose eigenstates are entangled. (This is the abridged version of @emiliopisanty's fine answer.) $\endgroup$ – WillO Nov 8 '17 at 15:36
  • $\begingroup$ Is the 'entanglement' an observable? No. $\endgroup$ – XXDD Nov 9 '17 at 6:22
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any measurement of the quantum system will collapse the system to the state which was the result of the measurement

This is correct, but irrelevant. It is possible to make entangled measurements (like, say, Bell state measurements) where all of the basis states are entangled, and the wavefunction collapse will send the system to an entangled state (and, just as importantly, tell you which entangled state you have).

More generally, what you're looking for is something called an entanglement witness: these are observables which, when measured can unambiguously certify that the states produced by a given preparation procedure are entangled.

That said, it's important to note that your conception of entanglement,

measuring one particle and then by the definition/concept of entanglement you will know the result of a measurement of the other particle

is blurry and ultimately inaccurate. Entanglement refers to a broad class of bipartite states that show correlations between measurement outcomes on the two systems (and which, moreover, can produce results for certain metrics of correlation that are impossible for classical systems), but the naive "if A is spin up then B is spin down" is too restrictive and fails to meaningfully demarcate the line between entanglement and classical correlations.

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