### Abstract

The Wigner-Araki-Yanase (WAY) theorem shows that additive conservation laws limit the accuracy of measurements. Recently, various quantitative expressions have been found for quantum limits on measurements induced by additive conservation laws, and have been applied to the study of fundamental limits on quantum-information processing. Here, we investigate generalizations of the WAY theorem to multiplicative conservation laws. The WAY theorem is extended to show that an observable not commuting with the modulus of, or equivalently the square of, a multiplicatively conserved quantity cannot be precisely measured. We also obtain a lower bound for the mean-square noise of a measurement in the presence of a multiplicatively conserved quantity. To overcome this noise it is necessary to make large the coefficient of variation (the so-called relative fluctuation), instead of the variance as is the case for additive conservation laws, of the conserved quantity in the apparatus.

Original language | English |
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Article number | 032106 |

Journal | Physical Review A - Atomic, Molecular, and Optical Physics |

Volume | 78 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2008 Sep 8 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics
- Physics and Astronomy(all)

### Cite this

*Physical Review A - Atomic, Molecular, and Optical Physics*,

*78*(3), [032106]. https://doi.org/10.1103/PhysRevA.78.032106

**Quantum limits of measurements induced by multiplicative conservation laws : Extension of the Wigner-Araki-Yanase theorem.** / Kimura, Gen; Meister, Bernhard K.; Ozawa, Masanao.

Research output: Contribution to journal › Article

*Physical Review A - Atomic, Molecular, and Optical Physics*, vol. 78, no. 3, 032106. https://doi.org/10.1103/PhysRevA.78.032106

}

TY - JOUR

T1 - Quantum limits of measurements induced by multiplicative conservation laws

T2 - Extension of the Wigner-Araki-Yanase theorem

AU - Kimura, Gen

AU - Meister, Bernhard K.

AU - Ozawa, Masanao

PY - 2008/9/8

Y1 - 2008/9/8

N2 - The Wigner-Araki-Yanase (WAY) theorem shows that additive conservation laws limit the accuracy of measurements. Recently, various quantitative expressions have been found for quantum limits on measurements induced by additive conservation laws, and have been applied to the study of fundamental limits on quantum-information processing. Here, we investigate generalizations of the WAY theorem to multiplicative conservation laws. The WAY theorem is extended to show that an observable not commuting with the modulus of, or equivalently the square of, a multiplicatively conserved quantity cannot be precisely measured. We also obtain a lower bound for the mean-square noise of a measurement in the presence of a multiplicatively conserved quantity. To overcome this noise it is necessary to make large the coefficient of variation (the so-called relative fluctuation), instead of the variance as is the case for additive conservation laws, of the conserved quantity in the apparatus.

AB - The Wigner-Araki-Yanase (WAY) theorem shows that additive conservation laws limit the accuracy of measurements. Recently, various quantitative expressions have been found for quantum limits on measurements induced by additive conservation laws, and have been applied to the study of fundamental limits on quantum-information processing. Here, we investigate generalizations of the WAY theorem to multiplicative conservation laws. The WAY theorem is extended to show that an observable not commuting with the modulus of, or equivalently the square of, a multiplicatively conserved quantity cannot be precisely measured. We also obtain a lower bound for the mean-square noise of a measurement in the presence of a multiplicatively conserved quantity. To overcome this noise it is necessary to make large the coefficient of variation (the so-called relative fluctuation), instead of the variance as is the case for additive conservation laws, of the conserved quantity in the apparatus.

UR - http://www.scopus.com/inward/record.url?scp=51649087705&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=51649087705&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.78.032106

DO - 10.1103/PhysRevA.78.032106

M3 - Article

VL - 78

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 3

M1 - 032106

ER -