Tighter uncertainty and reverse uncertainty relations

Debasis Mondal, Shrobona Bagchi, and Arun Kumar Pati
Phys. Rev. A 95, 052117 – Published 18 May 2017

Abstract

We prove a few state-dependent uncertainty relations for the product as well as the sum of variances of two incompatible observables. These uncertainty relations are shown to be tighter than the Robertson-Schrödinger uncertainty relation and other ones existing in the current literature. Also, we derive a state-dependent upper bound to the sum and the product of variances using the reverse Cauchy-Schwarz inequality and the Dunkl-Williams inequality. Our results suggest that not only can we not prepare quantum states for which two incompatible observables can have sharp values, but also we have both the lower and the upper limits on the variances of quantum mechanical observables at a fundamental level.

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  • Received 18 April 2017

DOI:https://doi.org/10.1103/PhysRevA.95.052117

©2017 American Physical Society

Physics Subject Headings (PhySH)

General PhysicsStatistical Physics & ThermodynamicsQuantum Information, Science & Technology

Authors & Affiliations

Debasis Mondal*, Shrobona Bagchi, and Arun Kumar Pati

  • Quantum Information and Computation Group, Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211019, India and Homi Bhabha National Institute, Anushaktinagar, Training School Complex, Mumbai 400085, India

  • *cqtdem@nus.edu.sg
  • shrobona@hri.res.in
  • akpati@hri.res.in

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Issue

Vol. 95, Iss. 5 — May 2017

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