[论文解读] The Hidden Nature of Non-Markovianity

Jihong Cai, Advith Govindarajan+1 more|arXiv (Cornell University)|Feb 19, 2026

Advanced Thermodynamics and Statistical Mechanics被引用 0

一句话总结

这篇论文表明任何可微的量子态轨迹都可以通过时变Markovian Lindbladian实现，意味着无法仅凭单一轨迹或有限路径样本推断出非马可夫性。

ABSTRACT

The theory of open quantum systems served as a tool to prepare entanglement at the beginning stage of quantum technology and more recently provides an important tool for state preparation. Dynamics given by time dependent Lindbladians are Markovian and lead to decoherence, decay of correlation and convergence to equilibrium. In contrast Non-Markovian evolutions can outperform their Markovian counterparts by enhancing memory. In this letter we compare the trajectories of Markovian and Non-Markovian evolutions starting from a fixed initial value. It turns out that under mild assumptions every trajectory can be obtained from a family of time dependent Lindbladians. Hence Non-Markovianity is invisible if single trajectories are concerned.

研究动机与目标

• Motivate the study of quantum non-Markovianity and its traditional trajectory-based perspectives.
• Demonstrate that differentiable state trajectories can be lifted to Markovian Lindbladian dynamics under mild regularity assumptions.
• Show that non-Markovianity is not detectable from single trajectories or finite ensembles and discuss implications for process identification.
• Clarify the geometric reasons behind trajectory indistinguishability and outline constructive lifting schemes for various classes of trajectories.

提出的方法

• Formulate the GKSL (Lindblad) time-local master equation as the Markovian framework.
• Prove Lindbladian lifting: any C2 path with mild spectral regularity admits a continuous Lindbladian lift (Theorem 1).
• Provide constructive criteria and explicit forms (replacer Lindbladians) to realize given trajectories as Markovian lifts.
• Use examples (pure dephasing trajectory) to illustrate how a Non-Markovian path can be realized by a Markovian generator.
• Discuss discrete-time sampling and show finite samples cannot certify non-Markovianity (piecewise affine interpolation results).
• Explain the tangent-cone geometry of state space and its role in lifting and indistinguishability results.]
• research_questions:[

Figure 1: The blue line shows a path of densities with tangent given by the green arrow. On the left we see that a jump operator with negative sign can lead out of the space of densities if the path hits the boundary. On the right we see that the derivative stays inside the space of densities if pat

实验结果

研究问题

• RQ1 Can every differentiable quantum trajectory be realized as the trajectory of a Markovian time-local Lindblad dynamics?
• RQ2 To what extent can non-Markovianity be inferred from a single trajectory or finite sets of trajectories?
• RQ3 What regularity conditions on a trajectory guarantee the existence of a Lindbladian lift?
• RQ4 How does the geometric structure of state space (tangent cone) explain trajectory indistinguishability between Markovian and Non-Markovian dynamics?
• RQ5 What are constructive methods to lift given trajectories to Markovian dynamics (e.g., replacer Lindbladians)?

主要发现

• Under mild regularity, every differentiable trajectory can be realized as the trajectory of a Markovian evolution via a Lindbladian lift (Theorem 1).
• A single trajectory generally cannot reveal non-Markovianity; many trajectories or full process information are required for identification.
• Even exponential families of trajectories can be realized by a single Markovian dynamics in product-space constructions.
• Finite discrete-time samples cannot distinguish Markovian from Non-Markovian evolutions, since piecewise affine paths admit Markovian realizations.
• The geometry of the state space—specifically the tangent cone—underpins why non-Markovianity is not identifiable from trajectory data alone.
• Lindbladian lifts can be constructed explicitly (e.g., replacer Lindbladians) and can be continuous under suitable rank-change conditions.