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arXiv · 2505.02914

Sequential Generation of Two-dimensional Super-area-law States with Local Parent Hamiltonian

Wucheng Zhang
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Abstract

We construct examples of highly entangled two-dimensional states by exploiting a correspondence between stochastic processes in $d$ dimensions and quantum states in $d+1$ dimensions. The entanglement structure of these states, which we explicitly calculate, can be tuned between area law, sub-volume law, and volume law. This correspondence also enables a sequential generation protocol: the states can be prepared through a series of unitary transformations acting on an auxiliary system. We also discuss the conditions under which these states have local, frustration-free parent Hamiltonians.

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Wucheng Zhang. 2025-05-05. Sequential Generation of Two-dimensional Super-area-law States with Local Parent Hamiltonian. https://doi.org/10.1103/t7py-glgv

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