Area law for steady states of detailed-balance local Lindbladians

Raz Firanko*, Moshe Goldstein, Itai Arad

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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.

Original languageEnglish
Article number051901
JournalJournal of Mathematical Physics
Volume65
Issue number5
DOIs
StatePublished - 1 May 2024

Funding

FundersFunder number
Israel Science Foundation
Directorate for Defense Research and Development3427/21
United States-Israel Binational Science Foundation1778/17, 2020072
Israel-Singapore NRF-ISF3528/20

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