Tomography is necessary for universal entanglement detection with single-copy observables

TitleTomography is necessary for universal entanglement detection with single-copy observables
Publication TypeJournal Article
Year of Publication2016
AuthorsLu, D, Xin, T, Yu, N, Ji, Z, Chen, J, Long, G, Baugh, J, Peng, X, Zeng, B, Laflamme, R
JournalPhysical Review Letters
Date Published2016/06/07

Entanglement, one of the central mysteries of quantum mechanics, plays an essential role in numerous applications of quantum information theory. A natural question of both theoretical and experimental importance is whether universal entanglement detection is possible without full state tomography. In this work, we prove a no-go theorem that rules out this possibility for any non-adaptive schemes that employ single-copy measurements only. We also examine in detail a previously implemented experiment, which claimed to detect entanglement of two-qubit states via adaptive single-copy measurements without full state tomography. By performing the experiment and analyzing the data, we demonstrate that the information gathered is indeed sufficient to reconstruct the state. These results reveal a fundamental limit for single-copy measurements in entanglement detection, and provides a general framework to study the detection of other interesting properties of quantum states, such as the positivity of partial transpose and the k-symmetric extendibility.