  Quantum field theory predicts the vacuum to exhibit a non-linear response to
strong electromagnetic fields. This fundamental tenet has remained
experimentally challenging and is yet to be tested in the laboratory. We
present proof of concept and detailed theoretical analysis of an experimental
setup for precision measurements of the quantum vacuum signal generated by the
collision of a brilliant x-ray probe with a high-intensity pump laser. The
signal features components polarised parallel and perpendicularly to the
incident x-ray probe. Our proof-of-concept measurements show that the
background can be efficiently suppressed by many orders of magnitude which
should not only facilitate a detection of the perpendicularly polarised
component of non-linear vacuum response, but even make the parallel polarised
component experimentally accessible for the first time. Remarkably, the angular
separation of the signal from the intense x-ray probe enables precision
measurements even in presence of pump fluctuations and alignment jitter. This
provides direct access to the low-energy constants governing light-by-light
scattering.
