Entanglement, partial set of measurements, and diagonality of the density matrix in the parton model

Abstract

We define the "entropy of ignorance" which quantifies the entropy associated with ability to perform only a partial set of measurement on a quantum system. For a parton model the entropy of ignorance is equal to a Boltzmann entropy of a classical system of partons. We analyze a calculable model used for describing low x gluons in Color Glass Condensate approach, which has similarities with the parton model of QCD. In this model we calculate the entropy of ignorance in the particle number basis as well as the entanglement entropy of the observable degrees of freedom. We find that the two are similar at high momenta, but differ by a factor of order unity at low momenta. This holds for the Renyi as well as von Neumann entropies. We conclude that the entanglement does not seem to play an important role in the context of the parton model.

11 pages, 1 figure; version accepted to Phys. Rev. D

References in corpus (6)

• The Color Glass Condensate
• The Color Glass Condensate density matrix: Lindblad evolution, entanglement entropy and Wigner functional
• Dynamical entropy of dense QCD states
• QCD Reggeon Field Theory for every day: Pomeron loops included
• From bubbles to foam: dilute to dense evolution of hadronic wave function at high energy
• The Color Glass Condensate and Glasma

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