Timeline for Bell's inequality for angles 120°
Current License: CC BY-SA 4.0
12 events
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| Oct 15, 2023 at 19:16 | comment | added | DrChinese | @Mauricio see my comment above. Indeed the violations occur at different angles for electrons vs. photons. The 120/120/120 case is not violated for electron spin, but is violated for photon polarization. | |
| Oct 15, 2023 at 10:50 | comment | added | Mauricio | Is this on photons or electrons? The angle might differ between the two... | |
| Oct 13, 2023 at 20:09 | comment | added | DrChinese | In keeping with several of the comments above: a) For a=0 degrees; b=45; c=90 you have |-.707 - 0| <=1+ -.707 which is then .707<=.293 and the Bell inequality IS violated. Or b) For a=0; b=120; c=240 you have |.5 - .5|<=1+ .5 which is 0<=1.5 and the inequality is NOT violated (agreeing with OP). Note that the b) angle settings are instead usually used for photon entanglement rather than electron entanglement, which does lead to a violation of an associated inequality. I believe the quantamagazine reference makes a technical error in their calculation of the QM expectation value. | |
| Oct 13, 2023 at 12:46 | history | edited | gandalf61 | CC BY-SA 4.0 |
added 247 characters in body
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| Oct 13, 2023 at 12:28 | comment | added | Norbert Schuch | ... (see e.g. Preskill's lecture notes, Chapter 4, where he derives a Bell inequality -- afaik the one from the original paper -- and precisely shows that it is violated by the 120-measurement (with opposite meas. directions for A and B) on a singlet state.) | |
| Oct 13, 2023 at 12:27 | comment | added | Norbert Schuch | Of course that's what Bell's theorem says (well, in fact it does not say that: It only says that this inequality is not violated for LHV models). Of course, for it to be non-trivial one should give one state where it is violated. Now the OP clearly says " And yet this example is often used to show a violation of Bell's inequality. ", so they think that this state should violate Bell's inequality. Whether it does depends how this inequality is defined, and from the question, this is certainly not clear. There is certainly one version of the inequality which is violated by that state ... | |
| Oct 13, 2023 at 12:22 | comment | added | gandalf61 | @NorbertSchuch No, no, no. The OP says that Bell's inequality is not violated in the $0,120,240$ case and they think it should be. But their calculation is correct - the inequality is not violated in the $0,120,240$ degrees case, but it does not need to be because Bell's theorem does not say the inequality is violated for all possible settings of the detectors, but only for some of them. | |
| Oct 13, 2023 at 12:14 | comment | added | Norbert Schuch | The OP claims that it is violated in this setting, and indeed, this is precisely what is usually said. The subtlety is that Alice's and Bob's axes have to be aligned the opposite direction, and I think this is precisely the OPs confusion. | |
| Oct 13, 2023 at 12:10 | comment | added | gandalf61 | @NorbertSchuch Can you show the calculation which demonstrates that Bell's inequality is violated when the detectors are set an angles $0, 120, 240$ degrees, so $P(a,b) = P(a,c) = P(b,c) = - \cos 120^o = \frac 1 2$ ? | |
| Oct 13, 2023 at 11:59 | comment | added | Pato Galmarini | yes, but I remember that for 120 angles it should be violated , also see quantamagazine.org/… | |
| Oct 13, 2023 at 11:28 | comment | added | Norbert Schuch | The standard Bell inequality is violated for the 120-degree alignment. There seems to be an error in the OPs calculation (or definitions), which needs to be clarified. | |
| Oct 13, 2023 at 7:05 | history | answered | gandalf61 | CC BY-SA 4.0 |