1. Quantum randomness and the device-independent claim Valerio Scarani Acknowledgment: Singapore MoE Academic Research Fund Tier 3 MOE2012- T3-1-009 “Random numbers from quantum processes” (June 2013-May 2018)

2. With quantum, you can! The unbelievable claim dilbert.com/strip/2001-10-25

3. The timeline of the claim Max Born: probabilistic interpretation of wave-function « Quantum mechanics calls for a great deal of respect. But some inner voice tells me that this is not the right track. The theory offers a lot, but it hardly brings us closer to the Old One’s secret. For my part at least, I am convinced He doesn’t throw dice. » Einstein to Born, November 1926 Werner Heisenberg: uncertainty relations, “microscope”  John Von Neumann: “no-go” theorem for “hidden variables” (flawed) Einstein-Podolski-Rosen argument Schrödinger’s cat metaphor Bell’s theorem Endorsed by Bohr and many others, rapidly becomes “orthodox”. Q-information First QRNGs Device-independent

4. More accurately… Bell’s theorem 1998 Mayers and Yao throw a great idea in the forest of complicated mathematics Ekert QKD based on Bell 1992 Bennett Brassard Mermin: Ekert = BB84 (for qubits of course!) Barrett Hardy Kent QKD secure beyond QM “Device-independent” QKD secure assuming only QM Tianmen mountains, Hunan province, China A lot ahead: rediscovering Mayers- Yao, semi-device- independent…, and of course RANDOMNESS Pragmatists quit: there is nothing more than old sound QM.

5. Outline of the talk Bell’s theorem, fast forward Concerns Two take-away observations Randomness may be a feature of our universe! Let’s observe it! Raphael, The school of Athens (1509)

6. Carra, The Red Horse (1912) Bell’s theorem, fast forward

7. Bell’s theorem: setting Two black boxes Possibility for the users to choose between two options. Can be pre-programmed together, but can’t communicate during the runs

8. Bell (1): hypothesis: pre-recorded output 0 output 1 +1 Hypothesis to be tested: the outcomes are pre-recorded Hypothesis to be tested: the outcomes are pre-recorded

9. Bell (2): mathematics a0 a1 b0 b1 In each run, you can read only (a0,b0), or (a1,b0), or (a0,b1) or (a1,b1), not S. But the average is: If (a0,a1,b0,b1) exist, S=+2 o S=-2 ✓

10. UNPREDICTABLE FOR ALL Bell’s theorem If (a0,a1,b0,b1) exist, then If one observes violation of the inequality, the assumption that the outcomes were pre-recorded is falsified. NOBODY could have known those numbers (if someone could, they could have written them in the boxes).

11. Device-independence & C. Bell’s criterion is: Device-independent Does not depend on the physical degrees of freedom being measured. Quantitative The more one violates, the more randomness is expected Quantum theory puts some limits on the violation (though the relation with the amount of randomness is not direct).

12. Experiments First attempts 1970s, not conclusive First clear evidence of violation: Aspect, 1982-3, with two entangled photons Since then, many more! –1998: Zeilinger switches, Gisin 10km –And not only with two photons: Two ions, two atoms… More than two photons –2015 Hanson “loophole-free” For physicists, the outcome was not in doubt Important technological step for DI

13. Concerns

14. The Physicists’ concern No-signaling? Can be pre-programmed together, but can’t communicate during the runs 1) Long distance Based on “nothing faster than light” Requires knowing when the choice is made, when the output is produced  2) Other reasonable arguments (For secrecy applications: trust that the provider has not hidden a radio in the boxes)

15. The Information-Theorists’ concern Input randomness? Possibility for the users to choose between two options. RANDOM FOR WHOM? The input must be random for the boxes, the output for the adversary. If non-adversarial provider: no problem. If adversarial provider: results on randomness expansion (still trust that there is no radio inside)

16. The Hackers’ concern Detection loophole? Sorry, I prefer not to answer that question +1 If that possibility is allowed, one can fake a violation of Bell with shared randomness! Operationally trivial to avoid: just force the boxes to commit to an outcome all the time. If no “physical detection”, output a pre- established value. But of course, if too many such instances, Bell won’t be violated any more

17. The Philosophers’ concern: (in)determinism? The many- worlds interpretation is deterministic! And so is Bohmian mechanics! And what if we are all in the Matrix?!? Yes, you can’t falsify full determinism with physics RANDOM FOR WHOM? Many worlds: determinism for a being who sees all the universes Bohm: determinism for a being who can read the unobservable pilot wave (nonlocal) For a being in our universe, violation of Bell implies randomness.

18. TWO take-away observations

19. A point of history Around the year 2000, QRNG were already commercial. Why did academic excitement start only after 2010? My answer: because to certify such a QRNG, you have to open it and know the physical process: no disruptive “quantum advantage” (unlike QKD, Shor) over physical RNGs based on physical noise. DI = quantum advantage to some QRNGs [Pironio et al. 2010, Colbeck-Kent 2011]

20. A point of logic and physics Bell inequalities are violated There is randomness in our universe There is more information in the statement “Bell is violated” than in the statement “there is randomness”. Wild shots: Anthropic? The universe is “designed” for us to certify randomness in a device-independent way. Nonlocal statistical laws? While long-distance is not an assumption of Bell per se, don’t dismiss “nonlocality” too quickly: those statistical processes, however they do it, they do it with no regard for space and time.

21. “There are more things in heaven and earth, Horatio, than are dreamt of in your philosophy.” (Hamlet, Act 1, Scene 5) http://xkcd.com/1591/