  Simply and reliably detecting and quantifying entanglement outside laboratory
conditions will be essential for future quantum information technologies. Here
we address this issue by proposing a method for generating expressions which
can perform this task between two parties who do not share a common reference
frame. These reference frame independent expressions only require simple local
measurements, which allows us to experimentally test them using an
off-the-shelf entangled photon source. We show that the values of these
expressions provide bounds on the concurrence of the state, and demonstrate
experimentally that these bounds are more reliable than values obtained from
state tomography since characterizing experimental errors is easier in our
setting. Furthermore, we apply this idea to other quantities, such as the Renyi
and von Neumann entropies, which are also more reliably calculated directly
from the raw data than from a tomographically reconstructed state. This
highlights the relevance of our approach for practical quantum information
applications that require entanglement.
