Symmetry from entanglement suppression

Symmetry is among the most fundamental and powerful concepts in nature, whose existence usually taken as given, without explanation. We explore whether symmetry can be derived from more principles perspective of quantum information. Starting with a two-qubit system, we show there are only two minimally entangling logic gates: Identity SWAP, where SWAP interchanges states qubits. further demonstrate that, when viewed an entanglement operator spin-space, $S$-matrix two-body scattering fermions $s$-wave channel uniquely determined by unitarity rotational invariance to linear combination SWAP. Realizing would give rise global symmetries, exemplified Wigner's spin-flavor Schr\"odinger's conformal low energy Quantum Chromodynamics. For $N_q$ species qubit, gate associated $[SU(2)]^{N_q}$ symmetry, which enlarged $SU(2N_q)$ species-universal coupling constant.