标题： 量子可访问信息和经典熵不等式 显示英文标题

标题： Quantum accessible information and classical entropy inequalities

摘要： 计算量子态集合的可访问信息是量子信息理论中的一个基本问题。 最近在[7]中获得的最优性准则，当应用于特定的态集合时，会导致香农熵的非平凡紧下界，这些下界是著名的对数 Sobolev 不等式的离散类比。 从这个角度来看，[2]中提出并数值验证的关于等角等概率态集合（量子金字塔）全局信息最优测量的假设被重新考虑，并提出了相应的紧熵不等式并予以证明。 通过最优性准则，这也提供了对[2]中提出的关于量子金字塔全局信息最优可观测量的猜想的第一个证明。 显示英文摘要

摘要： Computing accessible information for an ensemble of quantum states is a basic problem in quantum information theory. The optimality criterion recently obtained in [7], when applied to specific ensembles of states, leads to nontrivial tight lower bounds for the Shannon entropy that are discrete relatives of the famous log-Sobolev inequality. In this light, the hypothesis of globally information-optimal measurement for an ensemble of equiangular equiprobable states (quantum pyramids) put forward and numerically substantiated in [2] is reconsidered and the corresponding tight entropy inequalities are proposed and proved. Via the optimality criterion, this provides also the first proof of the conjecture concerning globally information-optimal observables for quantum pyramids put forward in [2].