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arXiv · 2403.20062

Non-invertible symmetries act locally by quantum operations

Masaki Okada·Yuji Tachikawa
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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.

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Masaki Okada, Yuji Tachikawa. 2024-03-29. Non-invertible symmetries act locally by quantum operations. https://doi.org/10.1103/physrevlett.133.191602

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