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A first meeting with Bell’s Experiments Valerio Scarani Centre for Quantum Technologies & Department of Physics, NUS

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MY FIRST QUANTUM SHOCK

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

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Indeed, all this is quantum: 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… In fact, all of physics (only gravity is unclear)

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

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

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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!

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

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EXPERIMENTS WITH PHOTONS

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Polarization of photons Classical light field Light = Electric field propagating as a transverse wave Polarization = direction of oscillation of the electric field Quantum light field 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. H-V basis+45/-45 basis

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How to measure polarization I Classical Quantum: 1 photon Polarizers = Filters Half intensity New polarization state I/2 I/4 I/2 0 p=1/2 « click » Transmitted Reflected

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Two “entangled” photons Laser Non-linear crystal

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“-1” Bell experiment Source of two entangled photons “+1” “-1” “+1” AliceBob

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

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

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Observations (3): Alice & Bob … … … … +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??

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

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

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Bell’s theorem: proof a Basis output a’ b Basis output b’ 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 = Part 2: 2. Proof: obvious

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Quantum violation of 2 Correlations of entangled photons (please believe me here): = cos(2( ) and for suitable choices of the measurements one can find = 2 2 > 2 Bell’s theorem: if the outcomes are agreed in advance, 2

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No mechanism!

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An experiment (Geneva, 1998) Cornavin Bellevue Bernex 4.5 km 7.3 km 10.9 km Classical channels R++ R-+ R+- R-- & KNbO 3 F laser LP Source d km 9.3 km quantum channel d 2 APD FS Z FM Z

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Results of the experiment Bell’s Thm: S 2 S(Q) = S(raw) = 2.41 S(net) = 2.7 >2 cos 2( )

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CONSEQUENCES

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Real randomness “+1” AliceBob Random!

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Secrecy “+1” AliceBob Private! “+1” Eve

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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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