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Experimentally exploring compressed sensing quantum tomography
In the light of the progress in quantum technologies, the task of verifying
the correct functioning of processes and obtaining accurate tomographic
information about quantum states becomes increasingly important. Compressed
sensing, a machinery derived from the theory of signal processing, has emerged
as a feasible tool to perform robust and significantly more resource-economical
quantum state tomography for intermediate-sized quantum systems. In this work,
we provide a comprehensive analysis of compressed sensing tomography in the
regime in which tomographically complete data is available with reliable
statistics from experimental observations of a multi-mode photonic
architecture. Due to the fact that the data is known with high statistical
significance, we are in a position to systematically explore the quality of
reconstruction depending on the number of employed measurement settings,
randomly selected from the complete set of data, and on different model
assumptions. We present and test a complete prescription to perform efficient
compressed sensing and are able to reliably use notions of model selection and
cross-validation to account for experimental imperfections and finite counting
statistics. Thus, we establish compressed sensing as an effective tool for
quantum state tomography, specifically suited for photonic systems.Comment: 12 pages, 5 figure
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