A new ranking of tests reveals how well they find entanglement

Akhil Kumar Awasthi of Harish-Chandra Research Institute and colleagues have established a performance ranking for tests designed to identify entanglement in quantum systems. Their work analyzes entropy-based, majorization, realignment and reduction criteria for detecting entanglement in random states, considering both the rank of the states and the size of the quantum subsystems involved. The researchers demonstrate that the realignment criterion is particularly effective when the dimensions of those subsystems are nearly equal, and they’ve proven lower bounds on the rank of quantum states beyond which realignment and entropic criteria will fail to detect entanglement. These results offer insights into the thresholds needed for reliable entanglement detection as complexity increases. This limitation is particularly relevant when analyzing high-rank entangled states within complex, high-dimensional systems, revealing inherent difficulties in identifying entanglement as dimensionality increases.…