Kavli Affiliate: Yuji Tachikawa
| First 5 Authors: Masaki Okada, Yuji Tachikawa, , ,
| Summary:
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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