1. SE Questions and progress in quantum information and causality
WS18/
Schüttelkopf Philipp

2. Overview Introduction Circuit Results Premise Causal relations Quantum
Realization
Setup
Witness
Results

3. Premise Example: drug trial A (treatment) precedes B (recovery)
A : assigned treatment D, treatment preference C
Berkson effect:
Classical: Given two independent events, if you consider only
outcomes where at least one occurs, then they become negatively dependent.
Here: Conditioned on recovery:
Assigned treatment and the unobserved common cause, also between assigned treatment and treatment preference

4. Cause effect Common cause Probabalistic mixture Physical mixture
Causal relations
Cause effect
Common cause
Probabalistic mixture
Physical mixture

5. Only interested in mixtures
Ignore combinations of quantum and classical
Coherent physical mixture:
Quantum Berkson effect

6. Quantum A and B quantum systems
Measurements on B and randomized intervention on A:
C is measured and D is randomly prepared
Trace-preserving, completely positive map from states on D to states on the composite C B:
Quantum Berkson effect:
Finding a measurement on B implies quantum correlations between C and D
Entanglement

7. Quantum classical Cause effect: Common cause Probabalistic mixture
Entanglement between B and D
Common cause
Entanglement between C and B
Probabalistic mixture
Physical mixture : if there exists no such probabalistic mixture

8. Realization Introduce E to mediate between B and C‘s common cause
Introduce F to preserve dimensionality, discarded afterwards
Initial state: =
Unitary: coherent combination of:
cause effect + common cause

9. Realization Map: identitiy D->B + CB in max entangled state
+ coherences
Berkson effect:
similarly
where:

10. Realization Probabalistic Quantum: Classical: PhysC
Replace the partial swap with an equal probabilistic
mixture of identity and swap
Eliminates coherence terms
Classical:
Complete Dephasing on D and E
Classical Bits
PhysC
B nontrivial function of D and E
Here: B = prob mixture[nontrivial-f(D,E) & max mixed state]

11. Setup i) no dephasing ii) dephasing BiBO... Bismuth-Borate
BBO ... β-Barium-Borate
LCR ... liquid-crystal retarder
HWP ...half-wave-plate
QWP ...quarter-wave-plate
APD ... avalanche photo diode
PBS/NPBS ... (Non)-polarizing beam splitter
Folded displaced Sagnac interferometer

12. Witness Physical mixture: Entanglement witness:
Is zero for all probabalistic mixtures
Entanglement witness:
Negativity
T ... Transposition
XYz = BDc (cause effect) , CBd (common cause)
Quantum Berkson effect:

13. Results a) and b) classical c) and d) quantum a) and c) prob mixtures
b) and d) phys mixtures
d) Quantum Berkson effect
(Uncertainties one standard deviation
Estimated using Monte Carlo, assuming
Poissonian noise, on photon counts)

14. Reconstructed causal maps Choi states
Real and imaginary part. Blue (red) represents positive (negative) values
Fidelities:
a) ProbC -
b) PhysC-
c) PhysQ -
d)COH -

15. Summary Common cause and cause effect are not mutually exclusive
Classically and quantum
Coherent/physical mixture if no probabalistic mixture
Quantum if Berkson correlations are quantum (entanglement)
Quantum coherent : each pathway (common-cause, cause-effect) coherent
Demonstrated to be realisable

16. Questions?