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.
Highlights
In recent years very interesting quantum information theory1 connections have begun to be explored in the context of high energy and nuclear physics
We ask if the relation suggested in Ref. [15] between the entropy in the parton model and the entropy of entanglement in a proton wave function exists in a computable model of a hadronic wave function frequently
We were able to reproduce the result of the previous calculations of the entanglement entropy which were performed in the field basis
Summary
In recent years very interesting quantum information theory connections have begun to be explored in the context of high energy and nuclear physics. Even considering more general measurements, such as those of double parton distributions, and possibly multiparton distributions one only probes the averages of the type ha†ðk1Þaðk1Þ...a†ðknÞaðknÞi All of these observables are diagonal in the number operator basis, and in principle carry no information about nondiagonal elements of the density matrix in this basis. The von Neuman entropy is strictly zero; if we ignore the off-diagonal elements of the density matrix and compute the entropy of ignorance the result is nonzero We will consider this interesting situation in the context of our model wave function below.
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