  As quantum technologies advance, the ability to generate increasingly large
quantum states has experienced rapid development. In this context, the
verification and estimation of large entangled systems represents one of the
main challenges in the employment of such systems for reliable quantum
information processing. Though the most complete technique is undoubtedly full
tomography, the inherent exponential increase of experimental and
post-processing resources with system size makes this approach infeasible even
at moderate scales. For this reason, there is currently an urgent need to
develop novel methods that surpass these limitations. This review article
presents novel techniques focusing on a fixed number of resources (sampling
complexity), and thus prove suitable for systems of arbitrary dimension.
Specifically, a probabilistic framework requiring at best only a single copy
for entanglement detection is reviewed, together with the concept of selective
quantum state tomography, which enables the estimation of arbitrary elements of
an unknown state with a number of copies that is low and independent of the
system's size. These hyper-efficient techniques define a dimensional
demarcation for partial tomography and open a path for novel applications.
