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.

中文翻译：

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不可逆对称性通过量子运算局部作用


量子场论和多体系统的不可逆对称性通过允许非可逆操作以及由群描述的更普通的可逆操作来推广对称性的概念。这封信的目的是指出，这些不可逆对称性通过量子运算作用于局部算子，即密度矩阵之间的完全正映射，它们形成了一类包含幺正演化和测量的自然运算，并在量子信息论中发挥着重要作用。这一观察结果将由一维量子 Ising 链的 Kramers-Wannier 对偶性来说明，这是不可逆对称操作的一个典型例子。