Area law for steady states of detailed-balance local Lindbladians

• URL: http://arxiv.org/abs/2212.10061v1
• Date: Tue, 20 Dec 2022 08:09:41 GMT
• Title: Area law for steady states of detailed-balance local Lindbladians
• Authors: Raz Firanko, Moshe Goldstein and Itai Arad
• Abstract summary: We study steady-states of quantum Markovian processes whose evolution is described by local Lindbladians. We show that under mild assumptions on the Lindbladian terms, the Lindbladian can be mapped to a local Hamiltonian on a doubled Hilbert space that has the same spectrum, and a ground state that is the vectorization of $sigma1/2$.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study steady-states of quantum Markovian processes whose evolution is described by local Lindbladians. We assume that the Lindbladian is gapped and satisfies quantum detailed balance with respect to a unique full-rank steady state $\sigma$. We show that under mild assumptions on the Lindbladian terms, which can be checked efficiently, the Lindbladian can be mapped to a local Hamiltonian on a doubled Hilbert space that has the same spectrum, and a ground state that is the vectorization of $\sigma^{1/2}$. Consequently, we can use Hamiltonian complexity tools to study the steady states of such open systems. In particular, we show an area-law in the mutual information for the steady state of such 1D systems, together with a tensor-network representation that can be found efficiently.

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