Testing complementarity on a transmon quantum processor

We propose quantum circuits to test interferometric complementarity using symmetric two-way interferometers coupled to a which-path detector. First, we consider the two-qubit setup in which the controlled transfer of path information to the detector subsystem depletes interference on the probed subspace, testing the visibility-distinguishability tradeoff via minimum-error state discrimination measurements. Next, we consider the quantum eraser setup, in which reading out path information in the right basis recovers an interference pattern. These experiments are then carried out in an IBM superconducting transmon processor. A detailed analysis of the results is provided. Despite finding good agreement with theory at a coarse level, we also identify small but persistent systematic deviations preventing the observation of full particlelike and wavelike statistics. We understand them by carefully modeling two-qubit gates, showing that even small coherent errors in their implementation preclude the observation of Bohr's strong formulation of complementarity.

Automated summary

In this study, quantum circuits are proposed to test interferometric complementarity, with experiments conducted in two different setups to explore the balance between visibility and distinguishability. Despite good agreement with theory at a coarse level, small systematic deviations were identified, preventing the observation of full particlelike and wavelike statistics. These deviations were attributed to small coherent errors in the implementation of two-qubit gates, which hinder the observation of Bohr's strong formulation of complementarity.