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Title: Position-momentum uncertainty relations in the presence of quantum memory

A prominent formulation of the uncertainty principle identifies the fundamental quantum feature that no particle may be prepared with certain outcomes for both position and momentum measurements. Often the statistical uncertainties are thereby measured in terms of entropies providing a clear operational interpretation in information theory and cryptography. Recently, entropic uncertainty relations have been used to show that the uncertainty can be reduced in the presence of entanglement and to prove security of quantum cryptographic tasks. However, much of this recent progress has been focused on observables with only a finite number of outcomes not including Heisenberg’s original setting of position and momentum observables. Here, we show entropic uncertainty relations for general observables with discrete but infinite or continuous spectrum that take into account the power of an entangled observer. As an illustration, we evaluate the uncertainty relations for position and momentum measurements, which is operationally significant in that it implies security of a quantum key distribution scheme based on homodyne detection of squeezed Gaussian states.
Authors:
 [1] ;  [2] ;  [3] ;  [4] ;  [5] ;  [6] ;  [6] ;  [7]
  1. Department of Physics, Graduate School of Science, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033 (Japan)
  2. Institute for Quantum Information and Matter, Caltech, Pasadena, California 91125 (United States)
  3. (Switzerland)
  4. School of Physics, The University of Sydney, Sydney 2006 (Australia)
  5. (Singapore)
  6. Institute for Theoretical Physics, ETH Zurich, Wolfgang-Pauli-Str. 27, 8093 Zürich (Switzerland)
  7. (Denmark)
Publication Date:
OSTI Identifier:
22403069
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 12; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CRYPTOGRAPHY; ENTROPY; INFORMATION THEORY; QUANTUM ENTANGLEMENT; SECURITY; UNCERTAINTY PRINCIPLE