报告人: 骆顺龙 研究员
骆顺龙，1989年毕业于上海交通大学，1995年获武汉大学博士学位，2001年任中国科学院数学与系统科学研究院研究员，博士生导师。现任中国科学院数学与系统科学研究院应用数学研究所所长，量子计算与量子信息处理研究中心主任, 北京数学会副理事长。曾应邀在第八届国际工业与应用数学大会作一小时大会报告 (2015)。主要从事概率统计﹑量子论和信息论研究。
Both coherence and uncertainty are fundamental concepts in quantum mechanics. We reveal some intrinsic and quantitative connections between them. In the resource theory, coherence is often quantified by distancelike quantities, among which a particularly convenient and intuitive quantifier of coherence is based on the Hilbert-Schmidt distance. This quantifier has a simple structure and many nice properties. Here we reveal its information-theoretic significance by showing that it coincides with uncertainty, as quantified by the variance of the state in the incoherent basis. The key point here is to regard the state as an observable, and to regard the incoherent basis as an ensemble of states rather than as measurement operators. Furthermore, in terms of the Tsallis 2-entropy, which is also a measure of uncertainty, we provide two alternative interpretations of coherence: as increase of uncertainty caused by decoherence and as the conditional Tsallis 2-entropy in the context of purification. An intrinsic relation between the maximal coherence and the Brukner-Zeilinger invariant information is also established. These identifications of coherence with increase of uncertainty lead us to interpret coherence as a manifestation of quantum uncertainty, which may have implications for both quantum foundations and applications.