Often, one can much more efficiently and cheaply estimate intricate properties of quantum systems without the need of full quantum state or process tomography. Using the idea of compressed sensing, even full quantum state tomography can be made for low rank states with about the square root of the previously known effort. Here, quantum information ideas are on the one hand guiding principles in work on signal processing. On the other, we provide key tools for certification in the quantum technologies, including benchmarking, certification and tomographic tools.

Selected group publications

• Quantum certification and benchmarking
  Nature Reviews Physics 2, 382 (2020)
  
• Semi-device-dependent blind quantum tomography
  arXiv:2006.03069
  
• A general framework for randomized benchmarking
  arXiv:2010.07974
  
• Quantum read-out for cold atomic quantum simulators
  Communications Physics 3, 12 (2020)
  
• Recovering quantum gates from few average gate fidelities
  Physical Review Letters 121, 170502 (2018)
  
• Randomized benchmarking for individual quantum gates
  Physical Review Letters 123, 060501 (2019)
  
• Quantum state tomography via compressed sensing
  Physical Review Letters 105, 150401 (2010)
  
• Towards experimental quantum field tomography with ultracold atoms
  Nature Communications 6, 7663 (2015)
  
• Experimental quantum compressed sensing for a seven-qubit system
  Nature Communications 8, 15305 (2017)
  
• Reliable quantum certification for photonic quantum technologies 
  Nature Communications 6, 8498 (2015)
• Measuring measurement
  Nature Physics 5, 27 (2009)
• Directly estimating non-classicality
  Physical Review Letters 106, 010403 (2011)
• Uncertainty quantification for matrix compressed sensing and quantum tomography problems
  arXiv:1504.03234
• Quantum tomography via compressed sensing: Error bounds, sample complexity, and efficient estimators
  New Journal of Physics 14, 095022 (2012)
• Assessing non-Markovian dynamics
  Physical Review Letters 101, 150402 (2008) 
• Information gain in tomography - a quantum signature of chaos
  Physical Review Letters 112, 014102 (2014)

Group reviews

• Quantum certification and benchmarking
  arXiv:1910.06343 (2019)