Mutually unbiased bases (MUBs) are a crucial ingredient for many protocols in quantum information processing. Measurements performed in these bases are unbiased to the maximally possible extent, which is used to prove the randomness or secrecy of measurement results. In this work we show that certain properties of sets of MUBs crucially depend on their specific choice, including, somewhat surprisingly, measurement outcome labeling. If measurements are chosen in a coherent way, the secrecy of the result can be completely lost for specific sets of MUB measurements but partially retained for others. This could potentially impact a broad spectrum of applications where MUBs are utilized.

中文翻译：

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选择互不偏倚的碱基和影响测量结果保密性的结果标签

相互无偏碱基（MUB）是量子信息处理中许多协议的重要组成部分。在这些基础上执行的测量在最大可能程度上不会产生偏差，这可用来证明测量结果的随机性或保密性。在这项工作中，我们表明，MUB集的某些属性至关重要地取决于其特定选择，包括令人惊讶的是测量结果标记。如果以连贯的方式选择测量，则对于特定的MUB测量集，结果的保密性可能会完全丢失，而对于其他MUB测量，则部分保留。这可能会影响使用MUB的广泛应用程序。