Sharing and verifying quantum informa3on with differing degrees of trust
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1 Sharing and verifying quantum informa3on with differing degrees of trust Damian Markham Paris Centre for Quantum Compu3ng pcqc.fr
2 Basics Measurements Random State ϕ Projector P r for result Proabibity for result r P r = I r Pr(r) = ϕ P r ϕ Change the state ρ r P r ϕ ϕ P r ϕ Entanglement Super correlations Push / Steer quantum information at a distance P A ϕ I B = ϕ A ϕ B ( 00 AB + 11 AB ) - Measuring A and B in same basis gives same result - Quantum state is transfered (Entanglement destroyed)
3 From philosophy to cryptography EPR 1935 This randomness is weird, we must be missing something a la statistical mechanics -> randomness from ignorance Bell 1964 If there really is a deterministic law of nature assigning measurement results (just we are ignorant of it) correlations are limited S = A, B + A, B' + A', B A', B' 2 -> QM gets S=2.14: no deterministic local model matches this Ekert 1991 If nature cannot predict the correlated results, neither can an eavesdropper! -> Secure shared random key Independent of physical model for correlations -> DEVICE INDEPENDENT SECURITY
4 Entanglement as a resource Z X P 0,1 or P +, P 0,1 or P +, Z X Quantum Key Distribution - Perfect correlations, not shared outside entangled pair (monogomy of entanglement)
5 Entanglement as a resource ϕ (Bell measurement with input ancilla) P ϕ, P Xϕ, P Yϕ, P Zϕ Classical measurement result ϕ Quantum Key Distribution - Perfect correlations, not shared outside entangled pair (monogomy of entanglement) Teleportation - Steers / pushes to state via Bell measurement: Quantum Channel
6 Entanglement as a resource Quantum Key Distribution - Perfect correlations, not shared outside entangled pair (monogomy of entanglement) Teleportation - Steers / pushes to state via Bell measurement: Quantum Channel Blind, verified computation - B does remote computation, without knowing A s measurement is blind to which computation he performs. - A can check the correlations, disabling from cheating Security from checking they share an entangled state
7 Different degrees of trust and fully trust their devices (know measurements) fully trusts her device, does not (only knows his sta3s3cs) Steering Neither nor trust their devices (only know sta3s3cs) Bell non-locality Jones, Wiseman, Doherty, PRA 2007
8 Different degrees of trust and fully trust their devices (know measurements) fully trusts her device, does not (only knows his sta3s3cs) Steering Correla3ons Measurement outomes Measurement senngs P(a, b A, B) = Tr( P a A P b Aρ Sep A,B) Trusted measurements Untrusted non- entangled states Neither nor trust their devices (only know sta3s3cs) Bell non-locality Jones, Wiseman, Doherty, PRA 2007
9 Different degrees of trust and fully trust their devices (know measurements) fully trusts her device, does not (only knows his sta3s3cs) Steering Neither nor trust their devices (only know sta3s3cs) Bell non-locality P(a, b A, B) = Correla3ons Measurement outomes Measurement senngs P(a, b A, B) = Tr( P a A P b Aρ Sep A,B) Trusted measurements λ Untrusted non- entangled states Predetermined (malicious) shared randomness Trusted measurement (A) Untrusted State on A P(λ) Tr( P a Aρ λ A)P(b Bλ) Untrusted measurement and states on B Jones, Wiseman, Doherty, PRA 2007
10 Different degrees of trust and fully trust their devices (know measurements) fully trusts her device, does not (only knows his sta3s3cs) Steering Neither nor trust their devices (only know sta3s3cs) Bell non-locality Jones, Wiseman, Doherty, PRA 2007 P(a, b A, B) = Correla3ons Measurement outomes Measurement senngs P(a, b A, B) = P(a, b A, B) = Tr( P a A P b Aρ Sep A,B) Trusted measurements λ λ Untrusted non- entangled states Predetermined (malicious) shared randomness Trusted measurement (A) Untrusted State on A P(λ) Tr( P a Aρ λ A)P(b Bλ) Untrusted measurement and states on B Predetermined (malicious) shared randomness P(λ) P(a Aλ)P(b Bλ) Untrusted (local) measurement and states on A and B
11 Different degrees of trust and fully trust their devices (know measurements) QKD Ent. Witnesses Quantum channel authen3ca3on Secure secret sharing (prac3cal authentn) fully trusts her device, does not (only knows his sta3s3cs) Steering 1- sided DI- QKD 1- sided DI ent. verifica3on FK verified blind universal QC Neither nor trust their devices (only know sta3s3cs) Bell non-locality Fully DI- QKD Bell inequality RUV verified blind universal QC
12 Different degrees of trust and fully trust their devices (know measurements) QKD Ent. Witnesses Quantum channel authen=ca=on Secure secret sharing (prac=cal authentn) Trust Difficulty fully trusts her device, does not (only knows his sta3s3cs) Steering 1- sided DI- QKD 1- sided DI ent. verifica=on FK verified blind universal QC Neither nor trust their devices (only know sta3s3cs) Bell non-locality Fully DI- QKD Bell inequality RUV verified blind universal QC
13 Different degrees of trust and fully trust their devices (know measurements) QKD Ent. Witnesses Quantum channel authen=ca=on Secure secret sharing (prac=cal authentn) Trust Difficulty fully trusts her device, does not (only knows his sta3s3cs) Steering 1- sided DI- QKD 1- sided DI ent. verifica=on FK verified blind universal QC Neither nor trust their devices (only know sta3s3cs) Bell non-locality Fully DI- QKD Bell inequality RUV verified blind universal QC
14 SQSS prac=cal Quantum Channel Authen=ca=on ϕ wants to share a secret with (or multiple s) such that - only can access the secret - is sure that receives the secret Resources - Shared secure classical key / authenticated classical channel Solved (for single ) [Barnum et al. FOCS 2002] - Uses error correcting codes - entanglement scales with security parameter (impractical!) We get linear security, but with no entanglement scaling (implemented!) - idea: mostly test entanglement and randomly decide where to teleport. Theory: Anne Marin and Damian Markham, ICITS Experiment: B. Bell, DM, D. Herrera- Mar3, A. Marin, W. Wadsworth, J. Rarity and M. Tame Nature Communica3ons 5, 5480 (2014)
15 SQSS prac=cal Quantum Channel Authen=ca=on Authen3cated classical channel Test Teleport Test Non- interac3ve ( to only) Eve assumed to control entangled pairs (but does not know which will be used to teleport) To pass all tests, must be perfect states, thus perfect channel Theory: Anne Marin and Damian Markham, ICITS Experiment: B. Bell, DM, D. Herrera- Mar3, A. Marin, W. Wadsworth, J. Rarity and M. Tame Nature Communica3ons 5, 5480 (2014)
16 SQSS prac=cal Quantum Channel Authen=ca=on Authen3cated classical channel Test Teleport Test Non- interac3ve ( to only) Eve assumed to control entangled pairs (but does not know which will be used to teleport) Test: Z X P 0,1 or P +, P 0,1 or P +, To pass all tests, must be perfect states, thus perfect channel Z X Theory: Anne Marin and Damian Markham, ICITS Experiment: B. Bell, DM, D. Herrera- Mar3, A. Marin, W. Wadsworth, J. Rarity and M. Tame Nature Communica3ons 5, 5480 (2014)
17 Security Projector Pass test = Projector entangled state + ½(guess!)! P ACC = I + φ + φ + $ # " 2 & % Prob (accept false state) < prob (used state is perfect entangled) ϕ ACC Prob (accept false state) = Tr( ( I B P B )ρ B ) Tr( ( I AB P φ + ) ρ ) ACC AB AB 1 S -> linear security -> practical!
18 Implementa=on Experiment implemen=ng (3,4), authen=cated secret sharing B. Bell, DM, D. Herrera- Mar3, A. Marin, W. Wadsworth, J. Rarity and M. Tame Nature Communica3ons 5, 5480 (2014)
19 Conclusions Most security in quantum information can be understood as verification of entanglement and non-locality Differing degrees of trust of devices permited by steering and nonlocality (semi and full device independent) Experimental demonstrations beyond QKD quantum crypto are appearing Next steps: -> Secure multiparty quantum computation -> Leader election -> Quantum money -> Verification of quantum simulation -> Verificaiton of quantum computation ->
20 Thank you! pcqc.fr FREQUENCY CIQWII HIPERCOM
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