High energy hadron interactions are commonly described by using a probabilistic parton model that ignores quantum entanglement present in the light-cone wave functions. Here, we argue that since a high energy interaction samples an instant snapshot of the hadron wave function, the phases of different Fock state wave functions cannot be measured—therefore the light-cone density matrix has to be traced over these unobservable phases. Performing this trace with the corresponding
U
(
1
)
Haar integration measure leads to ‘Haar scrambling’ of the density matrix, and to the emergence of entanglement entropy. This entanglement entropy is determined by the Fock state probability distribution, and is thus directly related to the parton structure functions. As proposed earlier, at large rapidity
η
the hadron state becomes maximally entangled, and the entanglement entropy is
S
E
∼
η
according to QCD evolution equations. When the phases of Fock state components are controlled, for example in spin asymmetry measurements, the Haar average cannot be performed, and the probabilistic parton description breaks down.
This article is part of the theme issue ‘Quantum technologies in particle physics’.
Entanglement, partial set of measurements, and diagonality of the density matrix in the parton model
