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。 我们表明，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，文献[2]中提出的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。 通过最优性准则，这也暗示了对文献[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. We show that 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. Via the optimality criterion, this suggests also a proof of the conjecture concerning globally information-optimal observables for quantum pyramids put forward in [2].