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arXiv · 2212.10061

Area law for steady states of detailed-balance local Lindbladians

Raz Firanko·Moshe Goldstein·Itai Arad
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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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Raz Firanko, Moshe Goldstein, Itai Arad. 2022-12-20. Area law for steady states of detailed-balance local Lindbladians. https://doi.org/10.1063/5.0167353

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