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Si-Ran Zhao, Shuai Zhao, Hai-Hao Dong, Wen-Zhao Liu, Jing-Ling Chen, Kai Chen, Qiang Zhang, Jian-Wei Pan

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*Bell's theorem states that quantum mechanical description on physical quantity cannot be fully explained by local realistic theories, and lays solid basis for various quantum information applications. Hardy's paradox is celebrated to be the simplest form of Bell's theorem concerning its "All versus Nothing" way to test local realism. However, due to experimental imperfections, existing tests of Hardy's paradox require additional assumptions of experimental systems, which constitute potential loopholes for faithfully testing local realistic theories. Here, we experimentally demonstrate Hardy's nonlocality through a photonic entanglement source.*"

The cited experiment was released a few days ago from a top team, closing both the locality loophole and the detection loophole in a test of Hardy's paradox. The observed value was close to the quantum prediction of .0004646 (small, yes, but above zero). The local realistic prediction is strictly <=0, and the highest value that was consistent with the local realistic prediction (given the actual results) was 10^-16348 (i.e. only about 16344 orders of magnitude too low).

This discussion is more about foundations than interpretations, but really touches on both. I have included some references on Hardy's Paradox for those who might be interested in learning more about this particular no-go theorem. Like GHZ, Hardy is an all-or-nothing no-go, and it implies that Quantum Mechanics is both nonlocal AND contextual. In other words: we should reject both locality* and realism.

Wiki: Hardy's Paradox

Detail version: Generalized Hardy's Paradox

Lay version of the above: Generalized Hardy's paradox shows an even stronger conflict between quantum and classical physics

My take: When cataloging the results of various modern tests of quantum theory and No-Go theorems of locality and/or realism, it is becoming clearer and clearer that a) purely local theories will not match experiment; and b) purely non-contextual (realistic/HV) theories will not match experiment.

Gleason 1957: reject non-contextuality

Bell 1964: reject local realism (some - such as Norsen - call it rejection of locality)

Bell-Kocken-Specker 1966-1967: reject non-contextuality/hidden variables

GHZ 1989: reject local realism (and both locality and realism, depending on your viewpoint)

Hardy 1993: reject local realism (and both locality and realism, depending on your viewpoint)

Leggett 2003: reject realism

PBR 2011: reject epistemic interpretations

Are there any interpretations still standing? ** *** Also: In each of the above No-Go works, the related experimental outcomes match traditional Quantum Mechanics - without any regard to Special Relativity at all. My conclusion is that adding relativistic considerations to QM does not in any way change the underlying foundations of essential theory. Otherwise, you would need to account for it in experiments. Clearly, relativistic considerations are unnecessary in all of the various no-go's and related experiments using entangled systems to test the concepts of Bell locality and realism/non-contextuality/hidden variables.

Putting together all of the above:

- a) "Relativity" is and must be respected in quantum physics; whereas "Locality" is not a feature of QM.
- b) Quantum Mechanics cannot be completed by hidden variables existing independently of the act of observation (i.e. choice of basis measurement).
- c) The wave function is "real" in the sense of PBR's "ontic".

*Of course I mean locality in the Bell sense (separable/factorizable), not in the sense of signal locality. From Nonlocality without inequalities for almost all entangled states of any quantum

system (Ghirardi, Marinatto, 2005) ****:

*"In the case in which the measurement processes take place at spacelike separated locations, the following condition demanding that all conceivable probability distributions of measurement processes satisfy the factorization property*

Pλ (Ai = a, Bj = b, . . . , Zk = z) = Pλ(Ai = a)Pλ(Bj = b). . . Pλ(Zk = z) ∀λ ∈ Λ (2)

*is a physically natural one which every hidden variable model is requested to satisfy. This factorizability request is commonly known as Bell’s locality condition [7]. We remark that all “nonlocality without inequalities” proofs aim at exhibiting a conflict between the quantum predictions for a specific entangled state and any local completion of quantum mechanics which goes beyond quantum mechanics itself. In fact, in the particular case in which the most complete specification of the state of a physical system is represented by the knowledge of the state vector |ψi alone, i.e., within ordinary quantum mechanics, the failure of the locality condition of Eq. (2) can be established directly by plugging into it appropriate quantum mechanical observables. Indeed, it is a well-known fact that for any entangled state there exist joint probabilities which do not factorize and, consequently, that*

**ordinary quantum mechanics is inherently a nonlocal theory**."** Simultaneous observation of quantum contextuality and quantum

nonlocality

This simply discusses many of the No-Go's mentioned above.

*** Interestingly (at least to me): Bohmian Mechanics is usually considered a nonlocal hidden variable (deterministic) theory. @Demystifier (one of our resident experts in Bohmian theory) told me once that he considers BM to be contextual. So deterministic *and* contextual! Apparently you can have it both ways! Of course, one of the complaints against the Bohmian side is precisely that no relativistic version has been successfully developed, while ordinary QM does have a relativistic versions (QFT).

**** Note that this title is the same as Hardy's original 1993 paper (on the same subject), as well as the same title as Sheldon Goldstein's 1993 paper (also on the same subject). I tried but was unable to locate PDFs of either of these.