  In 1935, in a paper entitled "Can quantum-mechanical description of reality
be considered complete?", Einstein, Podolsky, and Rosen (EPR) formulated an
apparent paradox of quantum theory. They considered two quantum systems that
were initially allowed to interact, and were then later separated. A
measurement of a physical observable performed on one system then had to have
an immediate effect on the conjugate observable in the other system - even if
the systems were causally disconnected! The authors viewed this as a clear
indication of the inconsistency of quantum mechanics. In the parton model of
the nucleon formulated by Bjorken, Feynman, and Gribov, the partons (quarks and
gluons) are viewed by an external hard probe as independent. The standard
argument is that, inside the nucleon boosted to an infinite-momentum frame, the
parton probed by a virtual photon with virtuality Q is causally disconnected
from the rest of the nucleon during the hard interaction. Yet, the parton and
the rest of the nucleon have to form a colour-singlet state due to colour
confinement, and so have to be in strongly correlated quantum states - we thus
encounter the EPR paradox at the sub-nucleonic scale. In this paper, we propose
a resolution of this paradox based on the quantum entanglement of partons. We
devise an experimental test of entanglement, and carry it out using data on
proton-proton collisions from the Large Hadron Collider (LHC). Our results
provide a strong direct indication of quantum entanglement at sub-nucleonic
scales.
