Quantum information approach to high energy interactions

TL;DR

This paper introduces a quantum information perspective to high energy hadron interactions, emphasizing the role of entanglement entropy derived from the hadron's wave function and its relation to parton structure functions.

Contribution

It demonstrates that tracing over unobservable phases in the light-cone wave function leads to entanglement entropy, linking quantum information concepts with high energy QCD phenomena.

Findings

Entanglement entropy is determined by Fock state probabilities.

At large rapidity, the hadron state becomes maximally entangled.

Quantum entanglement affects the validity of the probabilistic parton model.

Abstract

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 $\eta$ the hadron state becomes maximally entangled, and the entanglement entropy is $S_E \sim \eta$ 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.