Uncertainty relation between detection probability and energy fluctuations

Felix Thiel, Itay Mualem, David Kessler, Eli Barkai

Research output: Contribution to journalArticlepeer-review


A classical random walker starting on a node of a finite graph will always reach any other node since the search is ergodic, namely it fully explores space, hence the arrival probability is unity. For quantum walks, destructive interference may induce effectively non-ergodic features in such search processes. Under repeated projective local measurements, made on a target state, the final detection of the system is not guaranteed since the Hilbert space is split into a bright subspace and an orthogonal dark one. Using this we find an uncertainty relation for the deviations of the detection probability from its classical counterpart, in terms of the energy fluctuations.

Original languageEnglish
Article number595
Issue number5
StatePublished - 11 May 2021


  • Dark and bright states
  • Quantum search
  • Zeno subspaces, ergodicity

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Electrical and Electronic Engineering
  • Mathematical Physics
  • Physics and Astronomy (miscellaneous)


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