Entanglement growth in monitored systems. In particular we are interested in understanding how measurements during the dynamics can reduce the way in

受监控系统中的纠缠增长。

• 批准号: 2598090
• 金额: --
• 依托单位: King's College London
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2021
• 资助国家: 英国
• 起止时间: 2021 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2598090
• 关键词: Entanglement; growth; monitored; systems.; particular

Generically, the entanglement entropy of a quantum system grows under unitary dynamics (non interacting or interacting). Measurements of the systems local observables tends to reduce entanglement. It is a natural question to ask how do these two effects compete with one another and what is the resulting dynamics of the systems entanglement. This has been previously studied and is well understood in certain setups (Random unitary circuits with random projective measurements and free fermions with continuous local density monitoring for example) and has been shown to lead to interesting phenomena, e.g. entanglement phase transitions. It had been previously shown that for the free fermion example, the effective description of the dynamics is that of non-interacting bosons evolving with a non-hermitian effective Hamiltonian. Only the infinite time steady state under these dynamics for local measurements of lattice observables has been studied so we are interested in developing a dynamical description of the entanglement growth. We would also like to understand how the entanglement dynamics is different when the observables measured are coarse-grained over a number of lattice sites since the more coarse-grained the observables measured are the less information is gained about the system hence the entanglement is not reduced as much. The effective dynamics are non-interacting hence if the system is initialised in what is known as a Gaussian state, then the description of the dynamics can be reduced to a set of non-linear first order matrix differential equations for the correlation matrix . The entanglement dynamics can be computed using the correlation matrix using a well established tool called the 'quasiparticle picture' .

一般来说，量子系统的纠缠熵在幺正动力学（非相互作用或相互作用）下增长。对系统局部可观测量的测量往往会减少纠缠。这是一个自然的问题，问这两种效应如何相互竞争，以及系统纠缠的动力学是什么。这已经在以前研究过，并且在某些设置中得到了很好的理解（例如，具有随机投影测量的随机酉电路和具有连续局域密度监测的自由费米子），并且已经被证明会导致有趣的现象，例如纠缠相变。以前已经证明，对于自由费米子的例子，动力学的有效描述是非相互作用玻色子与非厄米有效哈密顿量的演化。只有在这些动力学下的无限时间的稳定状态的晶格观测的本地测量已被研究，所以我们有兴趣发展的纠缠增长的动力学描述。我们还想了解当测量的可观测量在多个晶格点上粗粒度时，纠缠动力学有何不同，因为测量的可观测量越粗粒度，获得的有关系统的信息就越少，因此纠缠度不会减少那么多。有效的动态是非相互作用的，因此，如果系统被初始化在所谓的高斯状态，那么动态的描述可以减少到一组非线性一阶矩阵微分方程的相关矩阵。纠缠动力学可以使用相关矩阵计算，使用一种被称为“准粒子图像”的成熟工具。