Given two orthonormal bases and , the basic form of the entropic uncertainty principle is stated in terms of the sum of the Shannon entropies of the probabilities of measuring and onto a given quantum state. State independent lower bounds for this sum encapsulate the degree of incompatibility of the observables diagonal in the and bases, and are usually derived by extracting as much information as possible from the unitary operator U connecting the two bases. Here we show a strategy to derive sequences of lower bounds based on alternating sequences of measurements onto and . The problem can be mapped into the multiple application of bistochastic processes that can be described by the powers of the unistochastic matrices directly derivable from U. By means of several examples we study the applicability of the method. The results obtained show that the strategy can allow for an advantage both in the pure state and in the mixed state scenario. The sequence of lower bounds is obtained with resources which are polynomial in the dimension of the underlying Hilbert space, and it is thus suitable for studying high dimensional cases.

给定两个正交基和，熵测不准原理的基本形式用测量概率和给定量子态的香农熵之和来表示。该和的状态无关下限封装了和基中可观察对角线的不相容程度，通常通过从连接两个基的酉算符U中提取尽可能多的信息来导出。在这里，我们展示了一种基于交替测量序列推导下界序列的策略。. 该问题可以映射到双随机过程的多重应用，可以通过直接从U导出的单随机矩阵的幂来描述。通过几个例子，我们研究了该方法的适用性。获得的结果表明，该策略在纯态和混合态场景中都具有优势。下界序列是用底层希尔伯特空间维度上的多项式资源获得的，因此适用于研究高维情况。