報告人: 駱順龍 研究員

講座日期：2021-07-12

講座時間：9:00

報告地點：數(shù)學與統(tǒng)計學院學術交流廳（文津樓3211）

主辦單位：數(shù)學與統(tǒng)計學院

講座人簡介：

駱順龍，1989年畢業(yè)于上海交通大學，1995年獲武漢大學博士學位，2001年任中國科學院數(shù)學與系統(tǒng)科學研究院研究員，博士生導師。現(xiàn)任中國科學院數(shù)學與系統(tǒng)科學研究院應用數(shù)學研究所所長，量子計算與量子信息處理研究中心主任, 北京數(shù)學會副理事長。曾應邀在第八屆國際工業(yè)與應用數(shù)學大會作一小時大會報告 (2015)。主要從事概率統(tǒng)計﹑量子論和信息論研究。

講座簡介：

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.