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Title: Uncertainty relation revisited from quantum estimation theory

Abstract

We use quantum estimation theory to formulate bounds of errors in quantum measurement for arbitrary quantum states and observables in a finite-dimensional Hilbert space. We prove that the measurement errors of two noncommuting observables satisfy Heisenberg-type uncertainty relation, find the achievable bound, and propose a strategy to achieve it.

Authors:
 [1];  [2];  [1]
  1. Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033 (Japan)
  2. Hakubi Center, Kyoto University, Yoshida-Ushinomiya-cho, Sakyo-ku, Kyoto 606-8302 (Japan)
Publication Date:
OSTI Identifier:
22080337
Resource Type:
Journal Article
Journal Name:
Physical Review. A
Additional Journal Information:
Journal Volume: 84; Journal Issue: 4; Other Information: (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1050-2947
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ERRORS; HILBERT SPACE; QUANTUM STATES; UNCERTAINTY PRINCIPLE

Citation Formats

Watanabe, Yu, Sagawa, Takahiro, Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwake-cho, Kyoto 606-8502, Ueda, Masahito, and ERATO Macroscopic Quantum Control Project, JST, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033. Uncertainty relation revisited from quantum estimation theory. United States: N. p., 2011. Web. doi:10.1103/PHYSREVA.84.042121.
Watanabe, Yu, Sagawa, Takahiro, Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwake-cho, Kyoto 606-8502, Ueda, Masahito, & ERATO Macroscopic Quantum Control Project, JST, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033. Uncertainty relation revisited from quantum estimation theory. United States. https://doi.org/10.1103/PHYSREVA.84.042121
Watanabe, Yu, Sagawa, Takahiro, Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwake-cho, Kyoto 606-8502, Ueda, Masahito, and ERATO Macroscopic Quantum Control Project, JST, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033. 2011. "Uncertainty relation revisited from quantum estimation theory". United States. https://doi.org/10.1103/PHYSREVA.84.042121.
@article{osti_22080337,
title = {Uncertainty relation revisited from quantum estimation theory},
author = {Watanabe, Yu and Sagawa, Takahiro and Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwake-cho, Kyoto 606-8502 and Ueda, Masahito and ERATO Macroscopic Quantum Control Project, JST, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033},
abstractNote = {We use quantum estimation theory to formulate bounds of errors in quantum measurement for arbitrary quantum states and observables in a finite-dimensional Hilbert space. We prove that the measurement errors of two noncommuting observables satisfy Heisenberg-type uncertainty relation, find the achievable bound, and propose a strategy to achieve it.},
doi = {10.1103/PHYSREVA.84.042121},
url = {https://www.osti.gov/biblio/22080337}, journal = {Physical Review. A},
issn = {1050-2947},
number = 4,
volume = 84,
place = {United States},
year = {Sat Oct 15 00:00:00 EDT 2011},
month = {Sat Oct 15 00:00:00 EDT 2011}
}