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

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JournalJournal of Physics A: Mathematical and Theoretical
DateSubmitted - Jan 2018
DateAccepted/In press - 23 May 2018
DateE-pub ahead of print - 7 Jun 2018
DatePublished (current) - 13 Jul 2018
Issue number28
Volume51
Number of pages34
Early online date7/06/18
Original languageEnglish

Abstract

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.

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© 2018 IOP Publishing Ltd. This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details

    Research areas

  • QUANTUM THEORY, quantum uncertainty, quantum measurement

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