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Updated: Jun 6, 2025

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
Published on: May 30, 2014
Noninvertible Symmetries Act Locally by Quantum Operations
Masaki Okada1, Yuji Tachikawa1
1<a href="https://ror.org/02chw6z69">Kavli Institute for the Physics and Mathematics of the Universe (WPI)</a>, University of Tokyo, Kashiwa, Chiba 277-8583, Japan.
Abstract:
Noninvertible symmetries of quantum field theories and many-body systems generalize the concept of symmetries by allowing noninvertible operations in addition to more ordinary invertible ones described by groups. The aim of this Letter is to point out that these noninvertible 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 noninvertible symmetry operations.
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