Measurement uncertainty relations: characterising optimal error bounds for qubits: Topical Review

Paul Busch, Thomas Joseph Bullock

Research output: Contribution to journalReview articlepeer-review


In standard formulations of the uncertainty principle, two fundamental features are typically cast as impossibility statements: two noncommuting observables cannot in general both be sharply defined (for the same state), nor can they be measured jointly. The pioneers of quantum mechanics were acutely aware and puzzled by this fact, and it motivated Heisenberg to seek a mitigation, which he formulated in his seminal paper of 1927. He provided intuitive arguments to show that the values of, say, the position and momentum of a particle can at least be unsharply defined, and they can be measured together provided some approximation errors are allowed. Only now, nine decades later, a working theory of approximate joint measurements is taking shape, leading to rigorous and experimentally testable formulations of associated error tradeoff relations. Here we briefly review this new development, explaining the concepts and steps taken in the construction of optimal joint approximations of pairs of incompatible observables. As a case study, we deduce measurement uncertainty relations for qubit observables using two distinct error measures. We provide an operational interpretation of the error bounds and discuss some of the first experimental tests of such relations.
Original languageEnglish
Number of pages34
JournalJournal of Physics A: Mathematical and Theoretical
Issue number28
Early online date7 Jun 2018
Publication statusPublished - 13 Jul 2018

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  • quantum uncertainty
  • quantum measurement

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