Quantum randomness and the device-independent claim

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

3. The timeline of the claim 1926 Max Born: probabilistic interpretation of wave-function Endorsed by Bohr and many others, rapidly becomes “orthodox”. 1927 Werner Heisenberg: uncertainty relations , “microscope” 1932 John Von Neumann: “no-go” theorem for “hidden variables” (flawed) 1935 Einstein-Podolski-Rosen argument Schrödinger’s cat metaphor Q-information 1964 1990 «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 Bell’s theorem First QRNGs 2000 Device-independent 2007

4. More accurately… A lot ahead: rediscovering Mayers-Yao, semi-device-independent…, and of course RANDOMNESS 1992 Bennett Brassard Mermin: Ekert = BB84 (for qubits of course!) Pragmatists quit: there is nothing more than old sound QM. 1998 Mayers and Yao throw a great idea in the forest of complicated mathematics 1991 1964 Ekert QKD based on Bell Bell’s theorem 2007 2005 “Device-independent” QKD secure assuming only QM Barrett Hardy Kent QKD secure beyond QM Tianmen mountains, Hunan province, China

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

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

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

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

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

10. 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). UNPREDICTABLE FOR ALL

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’ concernNo-signaling? • 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) Can be pre-programmed together, but can’t communicate during the runs

15. The Information-Theorists’ concernInput 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’ concernDetection loophole? • 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 +1 Sorry, I prefer not to answer that question

17. The Philosophers’ concern:(in)determinism? And what if we are all in the Matrix?!? The many-worlds interpretation is deterministic! 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. And so is Bohmian mechanics!

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/