From wikipedia:

For example, if a pair of entangled particles is generated such that their total spin is known to be zero, and one particle is found to have clockwise spin on a first axis, then the spin of the other particle, measured on the same axis, is found to be counterclockwise.

Yet the Bell tests all observe a lesser correlation:

If S is numerically greater than 2 it has infringed the CHSH inequality. The experiment is declared to have supported the QM prediction and ruled out all local hidden variable theories.

Is there any way to run an experiment that could observe (near) perfect correlation?


No. Tsirelson's bound states that, e.g., the value of $2\sqrt{2}$ obtained for the CHSH inequality is optimal within quantum theory, while the maximum value obtainable within all theories which cannot communicate instantly (no-signalling theories) would be 4.

  • $\begingroup$ Thanks, from the link: Significant research has been dedicated to finding a physical principle that explains why quantum correlations go only up to the Tsirelson bound and nothing more. I gather then that quantum entanglement is not "perfect", it sometimes happens and other times not? $\endgroup$ – Livid Feb 21 at 21:08
  • $\begingroup$ This has nothing to do with entanglement being perfect. Even perfect entanglement does not give you the maximal violation of Bell's inequality. If that's your definition of "perfect", then go with it, but I don't see a reason to do so. The wikipedia quote certainly does not justify your conclusion. $\endgroup$ – Norbert Schuch Feb 21 at 21:12
  • $\begingroup$ The point is that quantum theory - in fact, any theory where expectation values are associated to observables, and observables at different positions have to commute - cannot go beyond this bound. In some sense, this is rather perfect. (It has also been argued that this follows from rotational invariance of the theory, if I don't misremember arxiv.org/abs/quant-ph/0611001, so only a theory without the notion of continuous rotations - like classical bits - can give a larger violation.) $\endgroup$ – Norbert Schuch Feb 21 at 21:15
  • $\begingroup$ I apologize if I misunderstand the details of the test statistic and design of that particular type of experiment. By perfect I mean that the first wikipedia quote is accurate. Does that conservation of spin always happen when particles are entangled, or only sometimes? $\endgroup$ – Livid Feb 21 at 21:18
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    $\begingroup$ For the first quote you give, there is perfect entanglement which always gives perfect anticorrelation. But this is nothing quantum mechanical, you can observe perfect (anti-)correlation everywhere in our classical lives. (Just search for "Bertlmann's socks".) What is wrong is that you seem to assume that Bell tests measure the same type of correlations - they don't, they are designed to measure specifically quantum mechanical correlations (again, check Bertlmann's socks). $\endgroup$ – Norbert Schuch Feb 21 at 21:23

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