无信息贝叶斯量子测温
Uninformed Bayesian Quantum Thermometry
摘要：
我们研究贝叶斯测温方法，没有先验知识的预期温度范围内，通过能量测量的例子完全或部分热化量子位探针。我们发现，最常见的贝叶斯估计，即平均值和中位数，导致高温分歧时，用于不知情的测温。为了规避这一点，实现更好的整体精度，我们提出了两个新的估计的基础上优化的相对偏差。它们的全局温度平均行为与修改后的van Trees界相匹配，该界补充了较小探测数和无限制温度范围的Cramér-Rao界。此外，我们表明，使用部分热化探针，可以增加温度计的温度范围是敏感的本地精度的成本。
英文摘要：
We study the Bayesian approach to thermometry with no prior knowledge about the expected temperature scale, through the example of energy measurements on fully or partially thermalized qubit probes. We show that the most common Bayesian estimators, namely the mean and the median, lead to high-temperature divergences when used for uninformed thermometry. To circumvent this and achieve better overall accuracy, we propose two new estimators based on an optimization of relative deviations. Their global temperature-averaged behavior matches a modified van Trees bound, which complements the Cramér-Rao bound for smaller probe numbers and unrestricted temperature ranges. Furthermore, we show that, using partially thermalized probes, one can increase the range of temperatures to which the thermometer is sensitive at the cost of the local accuracy.
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