海森堡图像中不可逆量子动力学的可除性
Divisibility of Non-Invertible Quantum Dynamics in the Heisenberg Picture
- University of Turku（图尔库大学）
- Nicolaus Copernicus University（尼古拉·哥白尼大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文研究海森堡图像中不可逆量子动力学的可除性，证明CP可除性等价于算子范数单调性，刻画广义逆的完全正性障碍，并给出基于单位完全正投影的充分构造，且对量子比特动力学保证完全正广义逆传播子。
AI中文摘要：
我们研究了有限维量子动力学在海森堡图像中的可除性，此时动力学映射不必是可逆的。海森堡可除动力学在可达算子系统上确定了唯一的约化传播子，并且海森堡CP可除性被证明等价于算子范数单调性。尽管每个约化传播子都允许一个单位完全正扩展，但独立选择的扩展不一定满足复合律。广义逆在代数上恢复了该律，但通常不保持完全正性。我们刻画了由此产生的障碍，并基于可达算子系统上的单位完全正投影给出了一个充分构造。研究表明，对于量子比特动力学，海森堡CP可除性总是保证一个完全正的广义逆传播子。最后，我们分析了奇异时刻的时间局域生成元，并识别了动力学不可达方向上的相关规范自由度。
英文摘要：
We study divisibility of finite-dimensional quantum dynamics in the Heisenberg picture when the dynamical maps need not be invertible. Heisenberg divisible dynamics determines unique reduced propagators on the accessible operator systems, and Heisenberg CP-divisibility is shown to be equivalent to an operator-norm monotonicity. Although each reduced propagator admits a unital completely positive extension, independently chosen extensions need not satisfy a composition law. Generalized inverses restore this law algebraically, but do not, in general, preserve complete positivity. We characterize the resulting obstruction and give a sufficient construction based on unital completely positive projections onto the accessible operator systems. It is shown that for qubit dynamics Heisenberg CP-divisibility always guarantees a completely positive generalized-inverse propagator. Finally, we analyze time-local generators at singular times and identify the associated gauge freedom on dynamically inaccessible directions.
