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.

High energy QCD: Multiplicity distribution and entanglement entropy

“…We will show below that the McLerran-Venugopalan approach [25], which is used in Ref. [17], leads to the same multiplicity distribution as the parton cascade.…”

“…In Ref. [17], the density matrix is calculated in the CGC approach, using the CGC wave function from Refs. [49,50].…”

“…Over the past several years, new ideas have been developed in the high energy and nuclear physics community, which suggest a robust relation between the principle features of high energy scattering and entanglement properties of the hadronic wave function [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. The main idea, which we explore in this paper, is the intimate relation between the entropy in the parton approach [18][19][20][21] and the entropy of entanglement in a proton wave function [5].…”

“…The main difference between the CGC approach and the parton QCD cascade for the topics dealt with in this paper is the fact that the CGC approach generates the nondiagonal elements of the density matrix (see, for example, Refs. [3,9,12,17]), while for the parton cascade and, generally, in the BFKL Pomeron calculus, the density matrix is diagonal. Since in DIS experiments we can only measure the diagonal elements of density matrix, we can introduce in the framework another kind of entropy: "the entropy of ignorance" [17], which characterized this lack of knowledge of the actual density matrix in DIS experiments.…”

“…[3,9,12,17]), while for the parton cascade and, generally, in the BFKL Pomeron calculus, the density matrix is diagonal. Since in DIS experiments we can only measure the diagonal elements of density matrix, we can introduce in the framework another kind of entropy: "the entropy of ignorance" [17], which characterized this lack of knowledge of the actual density matrix in DIS experiments. We will show below that the McLerran-Venugopalan approach [25], which is used in Ref.…”