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Universality in Uncertainty Relations for a Quantum Particle

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Publication details

JournalJournal of Physics A: Mathematical and Theoretical
DateAccepted/In press - 23 Jun 2016
DatePublished (current) - 8 Aug 2016
Issue number35
Number of pages23
Original languageEnglish


A general theory of preparational uncertainty relations for a quantum particle in one spatial dimension is developed. We derive conditions which determine whether a given smooth function of the particle's variances and its covariance is bounded from below. Whenever a global minimum exists, an uncertainty relation has been obtained. The squeezed number states of a harmonic oscillator are found to be universal: no other pure or mixed states will saturate any such relation. Geometrically, we identify a convex uncertainty region in the space of second moments which is bounded by the inequality derived by Robertson and Schrödinger. Our approach provides a unified perspective on existing uncertainty relations for a single continuous variable, and it leads to new inequalities for second moments which can be checked experimentally.

Bibliographical note

© 2016, 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. Embargo period : 12 months

    Research areas

  • Heisenberg uncertainty relation, Robertson-Schrodinger uncertainty relation, preparational uncertainty relations, quantum harmonic oscillator, squeezed states, uncertainty relations

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