Related papers: Many-body chirality of topological stabilizer states

Many-body chirality of topological stabilizer states

URL: http://arxiv.org/abs/2606.20472v1
Date: Thu, 18 Jun 2026 16:52:26 GMT
Title: Many-body chirality of topological stabilizer states
Abstract summary: We introduce the notion of many-body chirality by formulating it as an obstruction to transforming a quantum state into its complex conjugate.<n>We reveal forms of chirality that evade conventional diagnostics, including vanishing modular commutator, vanishing chiral central charge, and commuting-projector realizations.<n>We prove that $mathbbZ_d(k)$ states with $d>2$ possess intrinsic many-body imaginarity.
Score: 7.245431345204559
License: http://creativecommons.org/licenses/by/4.0/
Abstract: A defining feature of chirality is the distinction between a system and its mirror image. Despite extensive experimental observations of chiral phases and theoretical advances, a quantum-information theoretic characterization of chirality based solely on the entanglement structure of many-body quantum states remains elusive. Here, we introduce the notion of many-body chirality by formulating it as an obstruction to transforming a quantum state into its complex conjugate through finite-depth local operations. We rigorously establish many-body chirality for stabilizer realizations of $\mathbb{Z}_d^{(k)}$ anyon theories, proving that complex conjugation can be implemented by local quantum channels if and only if the underlying anyon data are mirror invariant. This reveals forms of chirality that evade conventional diagnostics, including examples with vanishing modular commutator, vanishing chiral central charge, and commuting-projector realizations. We further show that this obstruction is intrinsically four-partite, while invisible to tripartite entanglement structure. Finally, we prove that $\mathbb{Z}_d^{(k)}$ states with $d>2$ possess intrinsic many-body imaginarity: their complex phase structure cannot be removed by finite-depth local unitaries. Remarkably, this includes states that are not many-body chiral.

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