近日，美国南加州大学的Paolo Zanardi&Faidon Andreadakis及其研究团队取得一项新进展。经过不懈努力，他们对量子动力学的算子空间纠缠力，与双酉电路中的局部算子纠缠增长进行了研究。相关研究成果已于2024年11月12日在国际知名学术期刊《物理评论A》上发表。

在这项工作中，研究人员引入一种度量方法，用于评估酉通道生成算符纠缠的能力，这代表了态空间纠缠能力在算符层面上的推广。通过最近提出的量子算符代数平均互易非交换性概念，研究人员证明了这种算符空间纠缠能力与酉通道的扰乱特性之间存在联系。研究人员确定了算符空间纠缠能力的上界，该上界对应于具有类似于典型酉矩阵扰乱特性的酉通道。

此外，在哈密顿动力学中，他们发现算符空间纠缠能力的短期增长率与双体非时序相关器的高斯扰乱率相匹配，从而在短时间尺度上建立了信息扰乱与算符纠缠生成之间的直接联系。最后，他们研究了跨越对称二分自旋链的局部算符纠缠的平均增长情况。对于双酉电路，结合分析和数值研究，他们发现局部算符纠缠的平均增长与构成块门的算符空间纠缠能力相关，并表现出两种不同的增长模式。

附：英文原文

Title: Operator space entangling power of quantum dynamics and local operator entanglement growth in dual-unitary circuits

Author: Faidon Andreadakis, Emanuel Dallas, Paolo Zanardi

Issue&Volume: 2024/11/12

Abstract: Operator entanglement is a well-established measure of operator complexity across a system bipartition. In this work, we introduce a measure of the ability of a unitary channel to generate operator entanglement, representing an operator-level generalization of the state-space entangling power. This operator space entangling power is demonstrated to be linked to the scrambling properties of the unitary channel via the recently introduced concept of mutual averaged noncommutativity of quantum operator algebras. An upper bound for the operator space entangling power is identified that corresponds to unitary channels with scrambling properties akin to those of typical unitaries. Additionally, for Hamiltonian dynamics, we find that the short-time growth rate of the operator space entangling power matches the Gaussian scrambling rate of the bipartite out-of-time-order correlator, establishing a direct link between information scrambling and operator entanglement generation for short timescales. Finally, we examine the average growth of local operator entanglement across a symmetric bipartition of a spin chain. For dual-unitary circuits, a combination of analytical and numerical investigations demonstrates that the average growth of local operator entanglement exhibits two distinct regimes in relation to the operator space entangling power of the building-block gate.

DOI: 10.1103/PhysRevA.110.052416

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.110.052416