Entanglement Suppression, Quantum Statistics and Symmetries in Spin-3/2 Baryon Scatterings

TL;DR

This paper investigates how entanglement suppression and quantum symmetries influence spin-3/2 baryon scatterings, revealing conditions under which the scattering matrix acts as quantum gates and exhibits enhanced symmetries.

Contribution

It introduces a novel analysis of entanglement power in baryon-baryon scattering, linking entanglement suppression to emergent symmetries and quantum gate interpretations.

Findings

Entanglement power vanishes when the S-matrix is an Identity or SWAP gate.

Enhanced symmetries emerge at minima of entanglement power, including SU(2s+1) for identical particles.

Constraints from spin statistics prevent zero entanglement power in identical particle scattering.

Abstract

We explore the interplay among entanglement suppression, quantum statistics and enhanced symmetries in the non-relativistic $S$-wave scattering involving the lowest-lying spin-3/2 baryons, which can be considered as four-dimensional qudits. These baryons form a ten-dimensional representation (decuplet) under the $\text{SU}(3)$ light-flavor symmetry and, in this limit, are considered indistinguishable under strong interactions. Treating the $S$-matrix in the spin-3/2 baryon-baryon scattering as a quantum logic gate in the spin space, we study the consequence of entanglement suppression and compute the entanglement power of the $S$-matrix. When the entanglement power vanishes, the $S$-matrix is either an Identity or a SWAP gate and spin-flavor symmetries and/or non-relativistic conformal invariance emerge, as previously observed in spin-1/2 baryons. In the case of scattering identical particles, the entanglement power never vanishes due to constraints from spin statistics, which we interpret as projection-valued measurements onto symmetric or antisymmetric Hilbert space and define the entanglement power accordingly. When the entanglement power is non-vanishing but sits at a global or local minimum, enhanced symmetries still emerge and the $S$-matrix can be interpreted as an Identity or a SWAP gate acting on the restricted Hilbert space allowed by quantum statistics. In general, when scattering identical spin-$s$ particles, we identify an enhanced $\text{SU}(2s+1)_{\text{spin}}$ symmetry for the Identity gate.