24aRG-8 Upper bound on our knowledge about noncommuting observables for a qubit system

Yuji Kurotani, Takahiro Sagawa, Masahito Ueda

A trade-off relation on our knowledge about two noncommuting observables of a qubit system in simultaneous measurement is formulated. The obtained inequality offers a quantitative information-theoretic representation of Bohr's principle of complementarity, and can be interpreted as a trade-off relation on the asymptotic accuracy of the maximum-likelihood estimation of the probability distributions of observables.

Mojtaba Jafarpour, Abbass Sabour

貴大 沙川, 雄司 黒谷, 正仁 上田

B. Rumbos

Xue‐Na Zhu, Shao-Ming Fei

Takahiro Sagawa, Yuji Kurotani, Masahito Ueda

We formulate the accuracy of quantum measurement for a qubit system in terms of a 3 by 3 matrix.This matrix, which we refer to as the accuracy matrix, can be calculated from a POVM corresponding to the quantum measurement.Based on the accuracy matrix, we derive new $trad\triangleright 0ff$ relations between the measurement accuracy of two or three noncommuting observables of a qubit system.These trade-off relations offer a quantitative information-theoretic representation of Bohr's principle of complementarity.We also show that the accuracy matrix is closely related to the maximum-likelihood estimation and the Fisher information matrix for a finite number of samples; the accuracy matrix tells us how accurately we can estimate the probability distributions of observables of an unknown state by quantum measurement.