  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.
