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.
@article{arxiv.quant-ph/0703130,
title = {Upper bound on our knowledge about noncommuting observables for a qubit system},
author = {Yuji Kurotani and Takahiro Sagawa and Masahito Ueda},
journal= {arXiv preprint arXiv:quant-ph/0703130},
year = {2009}
}