Area law for steady states of detailed-balance local Lindbladians
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866929344413171712 |
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| author | Firanko, Raz Goldstein, Moshe Arad, Itai |
| author_facet | Firanko, Raz Goldstein, Moshe Arad, Itai |
| contents | 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 $σ^{1/2}$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_10061 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Area law for steady states of detailed-balance local Lindbladians Firanko, Raz Goldstein, Moshe Arad, Itai Quantum Physics Mathematical Physics Atomic Physics 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 $σ^{1/2}$. 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. |
| title | Area law for steady states of detailed-balance local Lindbladians |
| topic | Quantum Physics Mathematical Physics Atomic Physics |
| url | https://arxiv.org/abs/2212.10061 |