Entropy and entanglement in polymer quantization

TL;DR

This paper investigates entropy and entanglement in polymer quantization, demonstrating convergence of entropy measures between standard and polymer Hilbert spaces as the polymer scale vanishes, and establishing bounds relating entropies across inequivalent representations.

Contribution

It provides a rigorous analysis of entropy convergence and bounds in polymer quantization, linking it to loop quantum gravity models.

Findings

Entropies of equivalent states converge as polymer scale approaches zero.

A general bound relates entropies in unitarily inequivalent representations.

Polymer quantization offers insights into quantum gravity models.

Abstract

Polymer quantization is as a useful toy model for the mathematical aspects of loop quantum gravity and is interesting in its own right. Analyzing entropies of physically equivalent states in the standard Hilbert space and the polymer Hilbert space we show that they converge in the limit of vanishing polymer scale. We derive a general bound that relates entropies of physically equivalent states in unitarily inequivalent representations.