No-go theorems for sequential preparation of two-dimensional chiral states via channel-state correspondence

TL;DR

This paper proves fundamental limitations on using sequential unitary circuits to prepare two-dimensional chiral states, showing that such states cannot be generated in Gaussian fermion systems or generic interacting systems through these methods.

Contribution

The paper establishes two no-go theorems demonstrating the impossibility of preparing 2D chiral states via sequential circuits in both Gaussian fermion and generic interacting systems.

Findings

Gaussian fermion chiral states cannot be generated by local translationally invariant channels.

Sequential circuits cannot produce the tripartite entanglement characteristic of chiral states.

Chiral states require non-local or non-sequential methods for their preparation.

Abstract

We investigate whether sequential unitary circuits can prepare two-dimensional chiral states, using a correspondence between sequentially prepared states, isometric tensor network states, and one-dimensional quantum channel circuits. We establish two no-go theorems, one for Gaussian fermion systems and one for generic interacting systems. In Gaussian fermion systems, the correspondence relates the defining features of chiral wave functions in their entanglement spectrum to the algebraic decaying correlations in the steady state of channel dynamics. We establish the no-go theorem by proving that local channel dynamics with translational invariance cannot support such correlations. As a direct implication, two-dimensional Gaussian fermion isometric tensor network states cannot support algebraically decaying correlations in all directions or represent a chiral state. In generic interacting systems, we establish a no-go theorem by showing that the state prepared by sequential circuits cannot host the tripartite entanglement of a chiral state due to the constraints from causality.