Quantum information approach to high energy interactions

Journal Article · 20 December 2021 · Philosophical Transactions of the Royal Society. A, Mathematical, Physical and Engineering Sciences

DOI: https://doi.org/10.1098/rsta.2021.0063 · OSTI ID:1832027

Kharzeev, Dima  ^[1]

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1. Stony Brook Univ., NY (United States); Brookhaven National Lab. (BNL), Upton, NY (United States)

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.

• Research Organization: Brookhaven National Laboratory (BNL), Upton, NY (United States); Stony Brook University, NY (United States)
• Sponsoring Organization: USDOE; USDOE Office of Science (SC), Nuclear Physics (NP)
• Grant/Contract Number: FG02-88ER40388; SC0012704
• OSTI ID: 1832027
• Report Number(s): BNL--222425-2021--JAAM
• Journal Information: Philosophical Transactions of the Royal Society. A, Mathematical, Physical and Engineering Sciences, Journal Name: Philosophical Transactions of the Royal Society. A, Mathematical, Physical and Engineering Sciences Journal Issue: 2216 Vol. 380; ISSN 1364-503X
• Publisher: The Royal Society PublishingCopyright Statement
• Country of Publication: United States
• Language: English