Erlangen 2018 – scientific programme

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Q: Fachverband Quantenoptik und Photonik

Q 40: Poster: Quantum Optics and Photonics III

Q 40.1: Poster

Tuesday, March 6, 2018, 16:15–18:15, Zelt West

Inferring two-qubit causal structures — •Jonas Kübler and Daniel Braun — Institut für theoretische Physik, Universität Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany

The rise of quantum information theory and machine learning has led to increasing interest in causal inference in quantum mechanics. Here we study a set-up proposed by Ried et al. [Nat. Phys. 11, 414 (2015)] in which a common-cause scenario can be mixed with a cause-effect scenario, and for which it was found that quantum mechanics can bring an advantage in distinguishing the two scenarios: Whereas in classical statistics, interventions such as randomized trials are needed, a pure observational scheme is enough to detect the causal structure if initial entanglement is available.
We analyze this setup in terms of the geometry of unital positive but not completely positive qubit-maps, arising from the mixture of qubit channels and steering maps. We find the range of mixing parameters interpolating between cause-effect and common-cause that can generate given correlation by establishing new bounds on signed singular values of sums of matrices. We prove a quantum advantage in a more general setup allowing arbitrary unital channels and initial states with fully mixed reduced states. Based on the geometry, we quantify the quantum advantage depending on the observed correlations and find the number of additional constraints needed for the complete solution of the causal inference problem.