We demonstrate that the LHC will be sensitive to quantum correlations between two quarks inside the proton. Same-sign W-boson pair production is the most promising channel for clear measurements of double parton scattering. The left-handed nature of the coupling between quarks and W-bosons makes it a prime probe to measure parton spin correlations. We perform a detailed analysis of double parton scattering, including relevant backgrounds. The analysis reveals that measurements comparing the rate at which two muons from W boson decays are produced in the same compared to opposite hemispheres are especially sensitive to spin correlations between two quarks inside the proton. We provide estimates of the significance of the measurements as a function of the integrated luminosity.