Entropic uncertainty relations and their applications

The Heisenberg uncertainty principle has a more precise formulation in terms of inequalities involving quantum entropies. Currently known entropic uncertainty relations are presented; they capture and extend Heisenberg's idea of the unpredictability of the outcomes of incompatible measurements. Distinct results are obtained for finite- and infinite-dimensional Hilbert spaces. Applications are surveyed, including the formulation of entanglement witnesses, current ideas about wave-particle duality, and the analysis of quantum cryptography.

• NS
  National Science Foundation

  Awards: PHY-1125565, 1125565
• GA
  Gordon and Betty Moore Foundation

  Awards: 12500028, PHY-1125565, GBMF-12500028
• SN
  Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung
• UO
  University of Sydney
• IC
  Industry Canada
• NO
  Nederlandse Organisatie voor Wetenschappelijk Onderzoek
• IF
  Institute for Quantum Information and Matter, California Institute of Technology

  Award: PHY-1125565
• NS
  Natural Sciences and Engineering Research Council of Canada
• ER
  European Research Council
• SV
  Stichting voor de Technische Wetenschappen
• AR
  Army Research Office

  Awards: W911NF-12-1-0521, W911NF
• SN
  Sandia National Laboratories