纠缠的不确定性原理
An uncertainty principle for entanglement
- University of British Columbia（不列颠哥伦比亚大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究针对二分希尔伯特空间中两个正交基，建立了弱纠缠与强纠缠态之间的定量不确定性原理，通过香农熵下界与Rényi熵差关联，并应用于限制弱纠缠态表示强纠缠哈密顿量基态的能力。
AI中文摘要：
考虑一个二分希尔伯特空间的两个正交基，使得一个基中的态是弱纠缠的，而另一个基中的态是强纠缠的。我们建立了以下不确定性原理的定量版本：在一个基中局域的每个态必须在另一个基中离域。更具体地说，我们将任何态在两个基中的系数分布的香农熵之和下界限制为它们的基态纠缠Rényi熵之差。该结果源于叠加纠缠的新的下界和上界，这些界可能具有独立的意义。作为应用，我们的结果限制了弱纠缠态在表示具有强纠缠能量本征态的哈密顿量的基态方面的能力。我们以Sachdev-Ye-Kitaev模型为例对此应用进行了数值说明。
英文摘要：
Consider two orthonormal bases of a bipartite Hilbert space such that states in one basis are weakly entangled and states in the other are strongly entangled. We establish a quantitative version of the following uncertainty principle: every state that is localized in one basis must be delocalized in the other. More specifically, we lower bound the sum of the Shannon entropies of any state's coefficient distributions in the two bases by the difference between the entanglement Rényi entropies of their basis states. The result follows from new lower and upper bounds on the entanglement of superpositions that may be of independent interest. As an application, our result limits the power of weakly-entangled states in representing ground states of Hamiltonians with strongly-entangled energy eigenstates. We illustrate this application numerically for the Sachdev-Ye-Kitaev model.
