  Tests of the predictions of quantum mechanics for entangled systems have
provided increasing evidence against local realistic theories. However, there
still remains the crucial challenge of simultaneously closing all major
loopholes - the locality, freedom-of-choice, and detection loopholes - in a
single experiment. An important sub-class of local realistic theories can be
tested with the concept of "steering". The term steering was introduced by
Schr\"odinger in 1935 for the fact that entanglement would seem to allow an
experimenter to remotely steer the state of a distant system as in the
Einstein-Podolsky-Rosen (EPR) argument. Einstein called this "spooky action at
a distance". EPR-Steering has recently been rigorously formulated as a quantum
information task opening it up to new experimental tests. Here, we present the
first loophole-free demonstration of EPR-steering by violating three-setting
quadratic steering inequality, tested with polarization entangled photons
shared between two distant laboratories. Our experiment demonstrates this
effect while simultaneously closing all loopholes: both the locality loophole
and a specific form of the freedom-of-choice loophole are closed by having a
large separation of the parties and using fast quantum random number
generators, and the fair-sampling loophole is closed by having high overall
detection efficiency. Thereby, we exclude - for the first time loophole-free -
an important class of local realistic theories considered by EPR. As well as
its foundational importance, loop-hole-free steering also allows the
distribution of quantum entanglement secure from an untrusted party.
