1. The device-independent outlook on quantum physics Definitions Part 1: History Part 2: self-testing
Valerio Scarani

2. Device-independent
How much entanglement?
How much randomness?
How much secret key?
Obtaining quantitative statements about the performance of a device without describing its physics.
If you need to rely on…
It’s a qubit
It’s light
The measurements are maximally unbiased
… then it’s not DI
This is possible thanks to classical tests of quantum behavior: Bell inequalities
Technical: we assume QM is valid (could be relaxed)

3. Characterization of the devices
Device-independent
Steering
Other partial relaxations
Tomography
Further refinement of assumptions: i.i.d./sequential/parallel repetition…

4. The adversary is another matter
Adversary = wants to learn your info (not “wants to destroy your device”)
Key distribution
Randomness
2-party crypto (e.g. bit commitment)
State characterization
Level of security
(power of the adversary):
“Unconditional”
Bounded storage
Classical side information
Polytime computation
… and many more

5. Examples Standard QKD (BB84 and the like)
Adversary: in the middle, unconditional
Device: fully characterised
DI Self-testing
Adversary: not required
Device: no-signaling black boxes = DI

6. The straight road to device-independence
Today
Bell 1964

7. The outcomes of a Bell test are certifiable random numbers
Bell violation
The results of the measurements did not pre-exist
Who could possibly have missed this straight argument?
Till 2005, basically everyone!
The outcomes of a Bell test are certifiable random numbers

8. CRYPTO
(Bennett-Brassard 1984)
NONLOCALITY
(Bell 1964; Aspect 1982)
Ekert 1991

9. No quantitative “security proof”, not even against individual attacks.

10. CRYPTO (Bennett-Brassard 1984) NONLOCALITY (Bell 1964; Aspect 1982)
Ekert 1991
BBM 1992
Entg-based protocols: context for security proofs in “standard QKD”:
Shor-Preskill 2000
Renner 2007

11. CRYPTO
(Bennett-Brassard 1984)
NONLOCALITY
(Bell 1964; Aspect 1982)
Ekert 1991
BBM 1992
Popescu & Rohrlich 1994

12. The PR-box can also be found in earlier works:
Rastall, Found. Phys. 1985
Summers & Werner, JMP 1987
Tsirelson, Hadron. Suppl. 1993
All are cited here! P&R wanted to make a nice point, not to claim discovery.
The PR-box

13. CRYPTO (Bennett-Brassard 1984) NONLOCALITY (Bell 1964; Aspect 1982)
Ekert 1991
BBM 1992
Popescu & Rohrlich 1994
Barrett-Hardy-Kent 2005
Renewed interest in PR-boxes in

14. No-signaling adversary
Zero key fraction (1 secret bit out of infinitely many signals, zero error)
[15] = BBM92

15. CRYPTO (Bennett-Brassard 1984) NONLOCALITY (Bell 1964; Aspect 1982)
Acin-Gisin-Masanes 2006
Equal only assuming qubits!
Ekert 1991
BBM 1992
Popescu & Rohrlich 1994
Barrett-Hardy-Kent 2005

16. Still against no-signaling adversary
Finite key fraction till 5% error (individual attacks)
Brings up explicitly the fact that the ideal correlations of BB84 are local: the “unconditional security” of that protocol must rely on assumptions on the devices

17. CRYPTO
(Bennett-Brassard 1984)
NONLOCALITY
(Bell 1964; Aspect 1982)
Ekert 1991
BBM 1992
Popescu & Rohrlich 1994
Barrett-Hardy-Kent 2005
Acin-Gisin-Masanes 2006
Acin et al “device-independent”

18. Against quantum adversary
Finite key fraction till 7% error (for collective attacks)

19. CRYPTO (Bennett-Brassard 1984) NONLOCALITY (Bell 1964; Aspect 1982)
Mayers-Yao 1998 “self-testing”
Werner-Summers 1987
Popescu Rohrlich 1992
Tsirelson 1993
Self-testing (see next)
Ekert 1991
BBM 1992
Popescu & Rohrlich 1994
Barrett-Hardy-Kent 2005
Acin-Gisin-Masanes 2006
Full security
Vazirani-Vidick 2014
Arnon-Friedmann et al. 2016
Randomness
Colbeck (+Kent) 2009
Pironio et al. 2010
Colbeck-Renner 2012
Dimension witnesses, partial DI…
Acin et al “device-independent”

20. FOCS98
Imperfect apparatus = one that overall does not work as you think, but works perfectly for the task.
Switch to “self-testing” in QIC2004
Ideal case only
Proof VERY hard to follow 
Do not mention the connection with nonlocality; E91 cited just as a pioneer alongside with BB84

21. Hadronic Journal Supplement 8, 329 (1993)
Focus on nonlocality, no connection with certification
Summers-Werner have some robustness bounds

22. CRYPTO (Bennett-Brassard 1984) NONLOCALITY (Bell 1964; Aspect 1982)
You owe a lot to your parents, but you are different
Mayers-Yao 1998 “self-testing”
Werner-Summers 1987
Popescu Rohrlich 1992
Tsirelson 1993
Self-testing (see next)
Ekert 1991
BBM 1992
Sometimes you are just too early…
Bell inequalities have a role to play (and not everything is a qubit)
Popescu & Rohrlich 1994
Barrett-Hardy-Kent 2005
Work on crazy stuff, ideas may come
Acin-Gisin-Masanes 2006
… but if the field is friendly, credit will be given 
Full security
Vazirani-Vidick 2014
Randomness
Colbeck (+Kent) 2009
Pironio et al. 2010
Colbeck-Renner 2012
Dimension witnesses, partial DI…
Acin et al “device-independent”

23. Summary of Part 1
The idea of device-independent certification is simple: violation of Bell implies non-classical randomness.
The path to get there was far from linear
Device-independent is about the characterization of the devices, not about the power of the adversary

24. Selected topic: device-independent self-testing
So, do you get those Mayers-Yao correlations?
Dad, here it says that CHSH is more robust!
Selected topic: device-independent self-testing
(you see, there is really no adversary!)

25. The geometric picture
Some extremal points of the set of correlations achievable with quantum physics can be obtained only from one state and the suitable measurements…
Mayers-Yao
… up to local isometries

26. Local isometry: pedestrian example
“junk” (may still contain entanglement)
Singlet ✓

27. Formalism of self-testing

28. In the lab x y a b Observed Assumptions No signaling
Quantum description (dimension not constrained)
All the conclusions must be derived from:
The observed P(a,b|x,y)
In the boxes there is an unknown pure state
In the boxes there are some unknown projectors.

29. Construct the isometry
Fidelity with the target state
(e.g. singlet)
Intuition: swap out the state you want to self-test
Important: you don’t need to implement this in the lab

30. Example: ideal self-test of the singlet (1) A possible isometry
Reminders
CNOT = Z-controlled application of X
Three inverted CNOTs = SWAP
Can we find
etc., such that l.h.s holds?

31. Example: ideal self-test of the singlet (2) Mayers-Yao criterion, McKague version
Hermitian, unitary
Mathematical construction

32. REVIEW OF RECENT RESULTS

33. All the self-testings of the singlet Y. Wang. X. Wu, VS, NJP 2016
2 parties, 2 inputs, 2 outputs:
P(a,b|x,y) self-tests the singlet if and only if
Mayers-Yao
CHSH:

34. Non-ideal self-testing: robustness Yang et al., PRL 2014; Bancal et al., PRA 2015
Case study: observed statistics = suitable measurements on Werner state
Bounds obtained with SDP based on the NPA hierarchy.
Lower bound
Mayers-Yao
CHSH
Last week’s arXiv by Kaniewski: applicable only to CHSH, but analytical!
Kurtsiefer highest CHSH =
Delft loophole free: CHSH=2.42

35. Versatility: beyond the singlet
All two-qubit pure entangled states [Bamps & Pironio PRA 2015]
CGLMP3: two-qutrit non-max entg state [Yang et al. PRL 2014]
Two or more singlets [Reichardt, Unger, Vazirani, Nature 2013, McKague 2015, Wu et al 2015]
Multipartite:
All graph states [McKague TQC’11]
Some three-qubit non-graph states [Wu et al, Pal et al, PRA 2014]
All of the above come with suitable measurements
Entangling measurements (e.g. Bell basis)

36. Parallel self-testing Wu, Bancal, McKague, VS, PRA 2016
Main challenge: we don’t assume the tensor product structure within each box
“Parallel”: not even sequential
“Double CHSH”
“Magic Square”
(upper bound)

37. Entangled measurement (1)
How can you prove that a measurement device has “entangled eigenstates” if it is a black-box? You don’t even know that there are subsystems, so what entanglement are we speaking about???
Well, it’s not really hopeless [Rabelo et al., PRL 2012]
Step 1 [ideal]
Step 2
A and B are uncorrelated
Inside C, there are two uncorrelated qubits!
The action of C has swapped the entanglement: C must have entangled the two qubits

38. Entangled measurement (2)
Robustness [Bancal et al. PRA 2015]:
Certifiable entanglement (negativity) of one of the eigenstates of C
The ideal case should give E=0.125: one must go far in NPA relaxation.

39. OPEN Questions & SUMMARY

40. Is self-testing “useful”?
Not for QKD, randomness & similar
If there is one figure of merit, optimize it directly!
To test “not-too-big” devices
Quality of a building block
Blind tomography (e.g. stabilizer states)
Alleged 1000-qubit quantum computers
As theoretical primitive (may be adversarial)
Interactive provers:
Reichardt-Unger-Vazirani, McKague, Fitzsimons, Hayashi…
Randomness expansion & amplification
Coudron-Yuen, Miller-Shi

41. Main challenges ahead Two big conjectures: Improve robustness
All pure states can be self-tested
Mixed states presumably can’t be self-tested, though we don’t have a clear proof either
All the extremal points of the quantum set of correlations self-test a state
Improve robustness
SDP is good, but analytical would be better
Apply to multi-copy (i.e. beyond i.i.d.)

42. Special for this workshop: An open question for channel lovers
“In the boxes, there is something that, when coupled to an ancilla, allows to extract the state”
“In the boxes, there is the state”
Not equivalent a priori:
Haagerup-Musat 2011
Yu-Duan-Xu 2012

43. Summary
Self-testing = “the signature of a quantum state” (and measurements)
Device independent
Recent:
Robust to imperfections
Versatile: various states and measurements
Future:
Many open questions.
Start using it to certify experiments.