Detecting entanglement in multipartite quantum states is an inherently probabilistic process, typically with a few measured samples. The level of confidence in entanglement detection quantifies the scheme’s validity via the probability that the signal comes from a separable state, offering a meaningful figure of merit for big datasets. Yet, with limited samples, avoiding experimental data misinterpretations requires considering not only the probabilities concerning separable states but also the probability that the signal came from an entangled state, i.e. the detection scheme’s efficiency. We demonstrate this explicitly and apply a general method to optimize both the validity and the efficiency in small data sets providing examples using at most 20 state copies. The method is based on an analytical model of finite statistics effects on correlation functions which takes into account both a Frequentist as well as a Bayesian approach and is applicable to arbitrary entanglement witnesses.

检测多部分量子态中的纠缠本质上是一个概率过程，通常需要几个测量样本。纠缠检测的置信度通过信号来自可分离状态的概率来量化该方案的有效性，为大数据集提供有意义的品质因数。然而，在样本有限的情况下，避免实验数据误解不仅需要考虑可分离态的概率，还需要考虑信号来自纠缠态的概率，即检测方案的效率。我们明确地证明了这一点，并应用一种通用方法来优化小数据集中的有效性和效率，提供最多使用 20 个状态副本的示例。该方法基于有限统计对相关函数影响的分析模型，该模型考虑了频率论和贝叶斯方法，并且适用于任意纠缠证人。