The measurement precision for two incompatible observables in a typical quantum system can be improved by the aid of one particle as a quantum memory. In this work, we study the entropic uncertainty relation in the presence of quantum memory (EUR-QM) and dense coding capacity (DCC) for arbitrary two-qubit X-states, and then we obtain an explicit relationship between the lower bound of the uncertainty and DCC. As an example, we examine the thermal EUR-QM as well as DCC in two kinds of two-qubit spin squeezing models (one-axis twisting model and two-axis counter-twisting model) under an external magnetic field. In the following, we relate EUR-QM to DCC and show analytically that there is an anti-correlated relation between them, and especially in the ground state. Our results show that for both the models, the entropic uncertainty and its bound can be decreased by reinforcing the spin squeezing parameters or decreasing the temperature of the system. Notably, we reveal that the val...

中文翻译：

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探索双量子X态的熵不确定性关系和密集编码能力

借助于一个粒子作为量子存储器，可以提高典型量子系统中两个不相容观测值的测量精度。在这项工作中，我们研究了在存在量子记忆（EUR-QM）和稠密编码能力（DCC）的情况下任意两个qubit X态的熵不确定性关系，然后获得了下界之间的明确关系。不确定性和DCC。例如，在外部磁场下，我们在两种双量子位自旋压缩模型（一轴扭曲模型和两轴反扭曲模型）中检查了热EUR-QM和DCC。在下文中，我们将EUR-QM与DCC相关联，并分析表明它们之间存在反相关关系，尤其是在基态下。我们的结果表明，对于这两个模型，可以通过增强自旋压缩参数或降低系统温度来降低熵不确定性及其边界。值得注意的是，我们发现该值...