通过广义Holevo-Curlander界对混合量子态最小错误区分度的双边估计
摘要
我们证明了任意混合量子态系综最优区分失败率的一个简洁的因子2估计，推广了Holevo [Theor. Probab. Appl. 23, 411 (1978)]和Curlander [博士论文，MIT，1979]的工作。对Cocha和Poor [Proceedings of the 6th International Conference on Quantum Communication, Measurement, and Computing (Rinton, Princeton, NJ, 2003)]的最小原理进行修改，推导出一个次优测量，其错误率通过构造在最优的因子2以内。该测量是二次加权的，并且作为Jezek等人[Phys. Rev. A 65, 060301 (2002)]提出的测量序列的第一次迭代出现。与所谓的“漂亮好测量”不同，在非等概率纯态情况下，它与Holevo的渐近最优测量一致。证明了Barnum和Knill [J. Math. Phys. 43, 2097 (2002)]测量界的一个二次加权版本。作为推论，得到了Schumacher和Westmoreland [Phys. Rev. A 56, 131 (1997)]意义上综合征可区分性的界。附录将我们的界与迹-Jensen不等式联系起来。
引用
@article{arxiv.0907.2094,
title = {Two-sided estimates of minimum-error distinguishability of mixed quantum states via generalized Holevo-Curlander bounds},
author = {Jon Tyson},
journal= {arXiv preprint arXiv:0907.2094},
year = {2009}
}
备注
It was not realized at the time of publication that the lower bound of Theorem 10 has a simple generalization using matrix monotonicity (See [J. Math. Phys. 50, 062102]). Furthermore, this generalization is a trivial variation of a previously-obtained bound of Ogawa and Nagaoka [IEEE Trans. Inf. Theory 45, 2486-2489 (1999)], which had been overlooked by the author