期刊
NEW JOURNAL OF PHYSICS
卷 18, 期 -, 页码 -出版社
IOP PUBLISHING LTD
DOI: 10.1088/1367-2630/18/8/083026
关键词
entanglement; area laws; tensor network states; Kolmogorov complexity
资金
- BMBF
- DFG [EI 519/7-1, CRC 183]
- EU
- ERC
It is commonly believed that area laws for entanglement entropies imply that a quantum many-body state can be faithfully represented by efficient tensor network states-a conjecture frequently stated in the context of numerical simulations and analytical considerations. In this work, we show that this is in general not the case, except in one-dimension. Weprove that the set of quantum many-body states that satisfy an area law for all Renyi entropies contains a subspace of exponential dimension. Wethen show that there are states satisfying area laws for all Renyi entropies but cannot be approximated by states with a classical description of small Kolmogorov complexity, including polynomial projected entangled pair states or states of multi-scale entanglement renormalisation. Not even a quantum computer with post-selection can efficiently prepare all quantum states fulfilling an area law, and we show that not all area law states can be eigenstates of local Hamiltonians. Wealso prove translationally and rotationally invariant instances of these results, and show a variation with decaying correlations using quantum error-correcting codes.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据