Compressed Sensing and QM: Recent Progress and State of the Art
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.
Subscribe to A Quantum Bit
Quantum physics began with revolutionary discoveries in the early twentieth century and continues to be central in today’s physics research. Learn about quantum physics, bit by bit. From definitions to the latest research, this is your portal. Subscribe to receive regular emails from the quantum world. Previous Issues...
Sign Up Now
Sign up to receive A Quantum Bit in your email!