Coherence-variance uncertainty relation and coherence cost for quantum measurement under conservation laws

Uncertainty relations are one of the fundamental principles in physics. It began as a fundamental limitation in quantum mechanics, and today the word {\it uncertainty relation} is a generic term for various trade-off relations in nature. In this letter, we improve the Kennard-Robertson uncertainty r...

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Bibliographic Details
Published inarXiv.org
Main Authors Tajima, Hiroyasu, Nagaoka, Hiroshi
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 06.09.2019
Subjects
Asymptotic methods
Coherence
Conservation laws
Quantum mechanics
Uncertainty
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Summary:Uncertainty relations are one of the fundamental principles in physics. It began as a fundamental limitation in quantum mechanics, and today the word {\it uncertainty relation} is a generic term for various trade-off relations in nature. In this letter, we improve the Kennard-Robertson uncertainty relation, and clarify how much coherence we need to implement quantum measurement under conservation laws. Our approach systematically improves and reproduces the previous various refinements of the Kennard-Robertson inequality. As a direct consequence of our inequalities, we improve a well-known limitation of quantum measurements, the Wigner-Araki-Yanase-Ozawa theorem. This improvement gives an asymptotic equality for the necessary and sufficient amount of coherence to implement a quantum measurement with the desired accuracy under conservation laws.
ISSN:2331-8422