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A first meeting with Bell’s Experiments

A first meeting with Bell’s Experiments. Valerio Scarani Centre for Quantum Technologies & Department of Physics, NUS. MY FIRST quantum SHOCK. Why is quantum hard?. “ Because it’s too theoretical”. It describes the largest variety of phenomena at the highest degree of precision!.

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A first meeting with Bell’s Experiments

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  1. A first meeting withBell’s Experiments Valerio Scarani Centre for Quantum Technologies & Department of Physics, NUS

  2. MY FIRST quantum SHOCK

  3. Why is quantum hard? “ Because it’s too theoretical” It describes the largest variety of phenomena at the highest degree of precision!

  4. Indeed, all of this is quantum: • Atomic and nuclear physics • From accelerators to power plants • Chemistry • Why H2O is stable? Why periodic table? • xx

  5. Indeed, all this is quantum: In fact, all of physics (only gravity is unclear) • Nuclei, atoms, molecules • All the particles discovered with accelerators… • The structure of the atoms, periodic table, radioactivity… • All of chemistry: why H2O is stable, why those reactions… • “Solid state” • Why Copper conducts current, why Iron is magnetic… • Semiconductors in your chips, superconductors in high speed trains, graphene… • Light • The universe • Big bang, cosmic background radiation • Energy of stars, and what happens when it finishes…

  6. Why is quantum hard? (2nd try) “Because one has to master a lot of mathematics before understanding” Understanding without maths is possible! Maths Understanding?? Ask students if they feel they understand it, after having learned about operators, eigenvalues and the like…

  7. “I can safely say that nobody understands quantum mechanics!” R.P. Feynman NI XIAO AH! LIM PEI UNDERSTAND QUANTUM PHYSICS! In fact, Feynman DID, and many other people DO, understand it. But… Maybe I can make a drawing? … you cannot “make a drawing”!

  8. User’s guide to the quantum world One cannot “make a drawing”, have a “mechanical” explanation  hard to grasp But this means that Nature is more interesting than we expected  It is worth while making the effort!

  9. A few relaxed days A few intense days One hour 1 minute 3 years Time/effort devoted by the target public This talk Classical analogs (light) MANY popular books Excellent textbooks

  10. Experiments with photons

  11. Classical light field Quantum light field Light = Electric field propagating as a transverse wave H-V basis Polarization = direction of oscillation of the electricfield +45/-45 basis Polarization of photons • light is « made » of photons • polarization is a property of each photon • the state of polarization of the photon determines the direction of oscillation of the macroscopic field.

  12. Polarizers = Filters Classical 0 I/2 I/2 I I/2 I/4 I/4 Quantum: 1 photon Transmitted Reflected p=1/2 • Half intensity • New polarization state p=1/2 « click » How to measure polarization The polarization of a photon cannot be learned with certainty

  13. Two “entangled” photons Laser Non-linear crystal

  14. Bell experiment “+1” “-1” “-1” “-1” “+1” “+1” Source of two entangled photons Alice Bob

  15. Observations (1): Alice +1 -1 -1 -1 +1 … +1 +1 -1 +1 -1 … -1 -1 -1 +1 +1 … Prob(+1|A) = Prob(-1|A) = ½, for all A Alice

  16. Observations (2): Bob -1 -1 +1 -1 +1 … +1 -1 -1 -1 +1 … -1 +1 +1 +1 -1 … Prob(+1|B) = Prob(-1|B) = ½, for all B Bob

  17. Observations (3): Alice & Bob +1 -1 -1 -1 +1 … +1 -1 -1 -1 +1 … -1 -1 +1 -1 +1 … -1 -1 +1 -1 +1 … -1 +1 +1 -1 -1 … -1 +1 +1 -1 -1 … -1 +1 +1 +1 -1 … -1 +1 +1 -1 -1 … -1 +1 -1 +1 -1 … -1 -1 +1 +1 -1 … Similar bases  “often” same results Distant bases  no correlation Same bases  same results CORRELATIONS AT A DISTANCE  HOW DO PHOTONS DO IT??

  18. Explanation, first attempt: communication Will do, tks Dear twin photon, I am going to be measured in the basis and shall give the result Pls behave accordingly. LOL Alice and Bob can be very distant: such a communication would have to propagate faster than the speed of light!

  19. Explanation, second attempt:previous agreement Basis  output Basis  output Basis  output Basis  output +1 -1 +1 -1 -1 +1 +1 -1 Nice! It explains same basis  same output +1 +1 +1 +1 It cannot explain the correlations for “similar” bases. The proof is based on “Bell’s theorem”.

  20. Bell’s theorem: proof Basis  output Basis  output b a b’ a’ Assumption: a, a’, b and b’ exist  one can compute: S = (a+a’)b + (a-a’)b’ Part 1: for all values of a, a’, b and b’, S=+2 or S=-2. Proof: if a=a’, …; and if a=-a’…  We cannot measure S in each shot, because we can choose only one basis; but we can measure <S> = <ab>+<a’b>+<ab’>-<a’b’> Part 2:<S>  2. Proof: obvious 

  21. Quantum violation of <S>2 Bell’s theorem: if the outcomes are agreed in advance, <S>2 Correlations of entangled photons (please believe me here): b a <ab> = cos(2(a-b)) and for suitable choices of the measurements one can find <S> = 22  2.8284 > 2

  22. No mechanism! • The outcomes: • are correlated at a distance • NOT through communication • NOT through agreement

  23. Bellevue 4.5 km a FM d 1 Z FM quantum channel + APD 1 8.1 km Cornavin - APD 1 10.9 km R++ F P L R-+ laser & Classical channels R+- R-- Source KNbO 3 - APD 2 9.3 km + APD 2 FS Z quantum channel b d 2 FS 7.3 km Bernex An experiment (Geneva, 1998)

  24. cos 2(a-b) 1.0 0.5 0.0 correlation coefficient >2 -0.5 V = (85.3 0.9)% ± raw V = (95.5 1) % ± net. 0 1000 4000 7000 10000 13000 time [sec] Results of the experiment Bell’s Thm: S 2 S(Q) = 2.8284 S(raw) = 2.41 S(net) = 2.7

  25. consequences

  26. Real randomness -1 +1 -1 +1 +1 “+1” +1 “+1” Random! Random! Alice Bob

  27. Secrecy -1 +1 -1 +1 +1 “+1” +1 “+1” Private! Private! Alice Eve Bob

  28. Summary • Quantum correlations EXIST • There is no “mechanism” that explains them • We can only predict probabilities • This is amazing… • … and is useful: randomness, secrecy

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