Non-invertible symmetries act locally by quantum operations

2024/03/29 by Masaki Okada, Yuji Tachikawa · 1 voice
Physics and Astronomy · #hep-th #cond-mat.str-el #quant-ph

paper · pdf · doi:10.1103/physrevlett.133.191602

arxiv published 2024/03/29 · arxiv updated 2024/11/07

Abstract

Non-invertible symmetries of quantum field theories and many-body systems generalize the concept of symmetries by allowing non-invertible operations in addition to more ordinary invertible ones described by groups. The aim of this paper is to point out that these non-invertible symmetries act on local operators by quantum operations, i.e. completely positive maps between density matrices, which form a natural class of operations containing both unitary evolutions and measurements and play an important role in quantum information theory. This observation will be illustrated by the Kramers--Wannier duality of the one-dimensional quantum Ising chain, which is a prototypical example of non-invertible symmetry operations.

Cited by

• Lattice Gauging Interfaces and Noninvertible Defects in Higher Dimensions
• Macroscopicity and observational deficit in states, operations, and correlations

Discussions

• Non-invertible symmetries act locally by quantum operations arxiv.org/abs/2403.20062 [bsky, 0 points, 0 comments]

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