Entanglement detection is of crucial significance to quantum technologies and yet remains a difficult enterprise. The positive partial transposition (PPT) and moment-based criteria are two key methods of entanglement detection. Among them, in an ideal setup, the PPT criterion can detect a greater volume of states but is more expensive, as it requires state tomography. We carry over the comparison of these two processes to a realistic situation with inaccurate detectors, in particular considering those that involve additional and lost counts. Considering Werner states, we find that the occurrence of additional counts does not result in false positives—declaring a separable state as entangled—for both methods. Additionally, we demonstrate that the PPT criterion detects a greater number of entangled Werner states compared to the moment-based method in this nonideal scenario. Moreover, we find that detectors troubled by lost counts may lead to false positives in both methods. However, the moment-based criterion is error free when the efficiency of the detectors is not significantly low; on the other hand, if the PPT criterion is used, a small deviation from the perfection of detectors can result in a wrong conclusion. The performance of the two criteria is further compared with both linear and nonlinear witness operators for Werner states. Nonlinear witness operators are found to be less accurate, whereas the linear witness achieves the same accuracy as the PPT criterion followed by tomography. Finally, we consider Bell mixture states and two-qubit pure entangled states mixed with white noise. For both, we observe that no erroneous detection of entanglement occurs only in the presence of additional counts, whereas false detection arises in the presence of lost counts for both the PPT and $p_3$-PPT criteria.

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• Entanglement detection
• Quantum entanglement
• Quantum foundations