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Compressed Sensing and QM: Recent Progress and State of the Art

March 9, 2016 - 11:00am
David Gross

Every time the release button of a digital camera is pressed, several megabytes of raw data are recorded. But the size of a typical jpeg output file is only 10% of that. What a waste! Can't we design a process which records only the relevant 10% of the data to begin with?
Compressed sensing is a young theory that achieves this trick for certain signals. There has been a fruitful exchange of ideas between this field and quantum physics: Mathematical methods from quantum information have found many applications in classical compressed data acquisition tasks. Conversely, compressed sensing ideas have advanced the theory of quantum state estimation. I will introduce the basics of the theory and outline where we stand with regards to quantum tomography applications. I will mention very recent results in uncertainty quantification, as well as applications of the diamond norm and the Clifford group in compressed sensing.

3100A Computer and Space Sciences
College Park, MD 20742