Freiburg 2019 – scientific programme

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FM: Fall Meeting

FM 36: Quantum Computation: Benchmarking and Certification

FM 36.8: Talk

Tuesday, September 24, 2019, 16:00–16:15, 2006

Blind tomography via sparse de-mixing — •Ingo Roth, Jadwiga Wilkens, Dominik Hangleiter, and Jens Eisert — Freie Universität, Berlin, Germany

The envisioned applications of quantum technologies require to achieve an enourmous precision in engineering its individual components. This is why efficient and flexible methods for extracting information about quantum devices from measurements are crucial. One important task is to fully determine a quantum state from the measured data, e.g. in order to improve devices for state preparation. Experimental schemes for quantum state tomography typically require measurement devices that are calibrated to a high precision. At the same time, the precision of the measurement's calibration ultimately relies on an accurate state preparation creating a vicious cycle. In this work, we develop the framework of blind tomography which breaks this vicious cycle using only very mild and generic structure assumptions. We propose a scheme allowing for incomplete knowledge of the measurement device during the tomography of a low-rank quantum state. The scheme simultaneously determines both the device's calibration and the quantum state with minimal resources and efficient classical post-processing. Building on recent techniques from the field of compressed sensing, we derive algorithmic strategies for blind tomography and provide analytical performance guarantees. We further demonstrate the performance of our scheme in numerical simulations.