Non-invertible symmetries act locally by quantum operations

• URL: http://arxiv.org/abs/2403.20062v2
• Date: Thu, 07 Nov 2024 09:04:19 GMT
• Title: Non-invertible symmetries act locally by quantum operations
• Authors: Masaki Okada, Yuji Tachikawa,
• Abstract summary: Non-invertible symmetries of quantum field theories and many-body systems generalize the concept of symmetries. Non-invertible symmetries act on local operators by quantum operations.
• Score: 0.552480439325792
• License:
• 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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