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

• URL: http://arxiv.org/abs/2505.02914v1
• Date: Mon, 05 May 2025 18:00:10 GMT
• Title: Sequential Generation of Two-dimensional Super-area-law States with Local Parent Hamiltonian
• Authors: Wucheng Zhang,
• Abstract summary: We construct examples of highly entangled two-dimensional states by exploiting a correspondence between processes in $d$ dimensions and quantum states in $d+1$ dimensions.<n>The entanglement structure of these states, which we explicitly calculate, can be tuned between area law, sub-volume law, and volume law.
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• License: http://creativecommons.org/licenses/by/4.0/
• 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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