QLunch: Blind Tomography via Compressed Sensing – University of Copenhagen

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QLunch: Blind Tomography via Compressed Sensing

Speaker: Ingo Roth, Freie Universität Berlin

Title: Blind Tomography via Compressed Sensing

Abstract: For the last 20 years, the research on quantum information processing is experiencing a rapid growth and holds great promises for revolutionary new technology. In the development of these quantum technologies efficient and flexibel methods for extracting information about a quantum state from measurements are required. One important task is to fully determine a quantum state from the measured data with only mild structure assumptions on the state. This is the problem of quantum state tomography. Using a signal processing paradigm called compressed sensing, quantum tomography schemes for low-rank states were developed that are resource-optimal. But to date compressed sensing schemes for quantum state tomography lack robustness against systematic imperfection of the measurement devices.

For this reason, experimental setups performing these schemes need to have measurement devices that are calibrated to a high precision. In this work we develop the framework of blind tomography which allows for incomplete knowledge of the measurement device during the tomography of a quantum state. The scheme simultaneously determines both the device 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 their performance in numerical simulations.