What is the Bell-like Inequality in Classical Physics?

[Heidi]

Hi Pfs
I read in the GHZ experiment article
that classical physics give an inéquality (a Bell like inequality)
Is there also sets of directions where this inequality is maximally violated ?
thanks

 

[DrChinese]

Hi Pfs
I read in the GHZ experiment article
that classical physics give an inéquality (a Bell like inequality)
Is there also sets of directions where this inequality is maximally violated ?
thanks

GHZ is often characterized as an "all or nothing" test. In principle, a single experimental run (of 3 total GHZ entangled photons) is enough to invalidate local realism.

It's a bit difficult to get that from the Wiki article, but here is the related quote they provide:

"For instance, if the polarization of two of the photons are measured and determined to be rotated +45° from horizontal, then local hidden variable theory predicts that the polarization of the third photon will also be +45° from horizontal. However, quantum mechanical theory predicts that it will be −45° from the same axis."

 

[Heidi]

Have we always 3 same outputs ,with a GHZ state, when we measure the same thing on the particles? linear polarization along a same direction, or same circular polarization?
or is GHZ HHH + VVV state on a given direction?

 

[gentzen]

Have we always 3 same outputs ,with a GHZ state, when we measure the same thing on the particles? linear polarization along a same direction, or same circular polarization?
or is GHZ HHH + VVV state on a given direction?

No, we don't always have 3 same outputs with a GHZ state. GHZ state is only HHH + VVV on a given direction. You can just try out a simple transformation to a specific other direction (like L/R instead of H/V) to see this:
(L+R)(L+R)(L+R) + (L-R)(L-R)(L-R) = 2LLL + 2LRR + 2RLR + 2RRL

 

[vanhees71]

Have a look at this Nature article. There it's explained in a very understandable way. The nice feature of the GHZ experiment is that it disproves the "local realism" a la EPR not with the violation of Bell inequality but disproving it by demonstrating that a certain observable takes the opposite value of what local realism predicts, of course in accordance with the prediction of QT:

https://www.nature.com/articles/35000514

 

[Heidi]

could you write the formulas of this article (with some comments)
the price of the article is too expensive (32 dollars)

 

[DrChinese]

could you write the formulas of this article (with some comments)
the price of the article is too expensive (32 dollars)

Here is the free version:

https://arxiv.org/abs/quant-ph/9810035