Symmetry from Entanglement Suppression

Abstract

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

arXiv comment4 pages + Supplementary Material; v2: minor revision to match the published version

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• Minimal Entanglement and Emergent Symmetries in Low-energy QCD
• Nuclear Forces for Precision Nuclear Physics -- a collection of perspectives
• Entanglement generation in few-nucleon scattering
• Entanglement between Valence and Sea Quarks in Hadrons of 1+1 Dimensional QCD