@article{fc1e2f59a12e45149a18e4a0f7533bfb,
title = "Area law for steady states of detailed-balance local Lindbladians",
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 σ. 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 σ1/2. 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.",
author = "Raz Firanko and Moshe Goldstein and Itai Arad",
note = "Publisher Copyright: {\textcopyright} 2024 Author(s).",
year = "2024",
month = may,
day = "1",
doi = "10.1063/5.0167353",
language = "אנגלית",
volume = "65",
journal = "Journal of Mathematical Physics",
issn = "0022-2488",
publisher = "American Institute of Physics",
number = "5",
}