Symmetry from Entanglement Suppression

TL;DR

This paper investigates how fundamental symmetries in physics can be derived from principles of quantum entanglement, showing that minimal entangling operations lead to known symmetries like SU(2) and SU(2N_q).

Contribution

It demonstrates that symmetries such as Wigner's spin-flavor and conformal invariance can emerge from the concept of minimal entanglement in quantum systems.

Findings

Only two minimally entangling two-qubit gates: Identity and SWAP.

The two-body fermionic S-matrix is uniquely determined by unitarity and rotational invariance.

Minimal entangling S-matrix leads to known physical symmetries.

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 Schr\"odinger'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.