Symmetry Breaking as Quantum Gate: Entropy and Weak Mixing Angle

TL;DR

This paper reveals a connection between entropic measures in electroweak interactions and interprets the weak mixing angle as a quantum gate operation, linking entropy and symmetry breaking.

Contribution

It establishes a novel correspondence between entropic probes and interprets the weak mixing angle as a quantum gate in chirality space.

Findings

RMI and SRE depend identically on  within each neutral-current channel.

The weak mixing angle  is linked to a quantum gate operation via Yukawa mass insertions.

Minimizing entropies yields  values matching axial vector-like couplings.

Abstract

We establish a correspondence between two independent entropic probes -- the variation of R\'{e}nyi mutual information (RMI) across the electroweak symmetry breaking (EWSB) transition and the stabilizer R\'enyi entropy (SRE) -- in tree-level $2\to 2$ elastic scatterings. After angular averaging, the RMI (helicity basis) and the SRE (fixed beam basis) exhibit identical dependence on $\sin^2\theta_W$ within each neutral-current channel. We trace this correspondence to a common physical origin that it's the Yukawa mass insertion acts as a $-\mathrm{i}Y$ quantum gate in chirality space. Minimizing entropies across all processes yields $\sin^2\theta_W$ values matching purely axial vector-like couplings in $Z$ boson exchanged channel.