Randomness extraction from Bell violation with continuous parametric - PowerPoint PPT Presentation

Randomness extraction from Bell violation with continuous parametric down conversion Lijiong Shen Jianwei Lee Alessandro Cer` e Le Phuc Thinh Valerio Scarani Christian Kurtsiefer Centre for Quantum Technologies Jean-Daniel Bancal University of Basel, CH Antia Lamas-Linares Texas Advanced Computing Center, USA Thomas Gerrits Adriana E. Lita Sae Woo Nam NIST, USA lijiong.shen@u.nus.edu

Secure private communication requires Randomness Classical systems cannot guarantee unpredictability https://en.wikipedia.org/wiki/RANDU

Secure private communication requires Randomness Classical systems cannot guarantee unpredictability https://en.wikipedia.org/wiki/RANDU

Non-classical correlations certify genuine randomness α x β y Alice Bob Correlation for measurement settings α x , β y E x , y = P ( a = b | x , y ) − P ( a � = b | x , y ) Bell parameter from 4 settings S = E 00 + E 01 + E 10 − E 11

bit/round 1 1 we are here 0 0 2 √ 2 | S | 0 0 2 2 2 2

Our point to the state of the art bits/s 114 10 2 1.8 10 0 .4 10 − 2 10 − 4 1.5e-5 year 2010 2013 2017 2018 S. Pironio et al., Nature (2010) B. G. Christensen et al., PRL (2013) Y.Liu et al., PRL (2018) P .Bierhorst et al.,Nature(2018)

Bell test with CW source and two detectors α x β y Alice Bob Alice time Bob

Bell test with CW source and two detectors α x β y Alice Bob + + + + + Alice time Bob

Correlation depends on bin width τ Alice time Bob

Correlation depends on bin width τ E = N ++ + N −− − N −+ − N +− = 2 N 3 + + + + + + + + + Alice time Bob = 30 s

Correlation depends on bin width τ E = N ++ + N −− − N −+ − N +− = − 1 N 9 + + + + + + + + + + + Alice time Bob = 20 s

Experimental setup LD@405nm SMF@810nm SMF PM @405nm HWP HWP@45 SMF-28e PBS PBS P P K T φ P θ TES timestamp PBS HWP@45 efficiency > 98 % | ψ � = cos θ | HV � − e i φ sin θ | VH � jitter ≈ 170 ns P . H. Eberhard, Phys. Rev.A(1993)

Pair generation rate ≈ 24 000 / s for 5 mW of UV pump 45.7 dark count/s 0 19.8 24 kcps Alice 82.4% Bob 82.2% 41.5 2 / 3

Optimal setting for loophole free Bell test - State | ψ � ≈ 0 . 9 | HV � − 0 . 43 | VH � HH HV VH VV HH HV VH VV

Optimal setting for loophole free Bell test - State | ψ � ≈ 0 . 9 | HV � − 0 . 43 | VH � HH HV VH VV HH HV VH VV

Optimal setting for loophole free Bell test - Projections β 0 = 82 . 7 ◦ β 1 = 61 . 5 ◦ α 1 = 28 . 7 ◦ α 0 = 7 . 2 ◦

We observe a violation of S = 2 . 01602 ( 32 ) ( S − 2 ) × 10 − 3 16.02 simulation experiment 0 0 bin width ( µ s) 13.15 ≈ 0 . 32 pairs/round

Rate of randomness bit/round round/s × 0 0 τ τ

Rate of randomness kbits/s 1.93 1.32 s i m u l e a x t i p o e n r i m e n t 0 0 . 9 4.4 27 bin width ( µ s)

Finite statistics - Block extraction m = n · η opt ( ε c , ε s ) + 4 log ǫ EX − 10 n We choose ε c = ε s = 10 − 10 Trevisan extractor based on polynomial hashing with block weak design

In 26 min we generated 617 920 random bits (396 bits/s) ⇒

Processing time for 26mins data 26 mins data ↓ 9 hours processing

Processing time for 10 hours data 10 hours data ↓ 28 years processing Toeplitz extractor ↓ 943 bits/s in few hours

Our point to the state of the art bits/s 943 396 114 10 2 1.8 10 0 .4 10 − 2 10 − 4 1.5e-5 year 2010 2013 2017 2018 S. Pironio et al., Nature (2010) B. G. Christensen et al., PRL (2013) Y.Liu et al., PRL (2018) P .Bierhorst et al.,Nature(2018)

Conclusion α x β y 2.01602 a b + + + + + Alice 2 time Bob 1.32 kbit/s arXiv:1805.02828 bin width lijiong.shen@u.nus.edu

lijiong.shen@u.nus.edu

SUZHOU lijiong.shen@u.nus.edu

Observed violation changes with τ S violation 2 2 simulation experiment 1.12 1.12 bin width ( µ s) 0 0 1000 1000 2000 2000 ≈ 24 pairs/round

Rate of randomness with finite block size kbits/s 1.93 n → inf 1.32 1.14 n = 10 10 .83 n = 10 9 s i m n = 10 8 u l a t 0.16 i o n 0 bin width ( µ s) 4.4 5.6 7.3 12.1