论文标题
详细的稳定状态的当地林金牌人的区域法
Area law for steady states of detailed-balance local Lindbladians
论文作者
论文摘要
我们研究了量子马尔可夫过程的稳态，其进化是由局部lindbladians描述的。我们假设Lindbladian被盖开并满足量子详细的平衡，相对于独特的全等级稳态$σ$。我们表明，在林德布拉德术语中的轻度假设下，可以有效地检查，林德布拉德人可以在具有相同频谱的双倍的希尔伯特空间上映射到当地的哈密顿量，并且是$σ^{1/2} $的矢量化。因此，我们可以使用哈密顿复杂性工具来研究这种开放系统的稳态。特别是，我们显示了此类1D系统稳态的共同信息中的一个区域法，以及可以有效发现的张量 - 网络表示。
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.
