SE Questions and progress in quantum information and causality WS18/19 11.04.2019 Schüttelkopf Philipp

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

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

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

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

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

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

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

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

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]

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

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:

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)

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

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

Questions?