Jihong Cai | Searcharxiv

arXiv2026

The Hidden Nature of Non-Markovianity

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.

quant-ph↗

arXiv2025

How Far do Lindbladians Go?

We study controllability of finite-dimensional open quantum systems under a general Markovian control model combining full coherent (unitary) control with tunable dissipative channels. Assuming the Hamiltonian controls is a Hörmander system that generate $\mathfrak{su}(n)$, we ask how little dissipation suffices to make the full state space $\mathcal{D}(\mathcal{H})$ controllable. We show that minimal non-unital noise can break unitary-orbit invariants and, in many cases, a very small set of jump operators yields transitivity on $\mathcal{D}(\mathcal{H})$. For multi-qubit systems we prove explicit transitivity results for natural resources such as a single-qubit amplitude-damping jump together with a dephasing channel, and we identify obstructions when only self-adjoint jump operators are available (yielding only unital evolutions). We further develop a geometric viewpoint and ask the ``lifting'' question: when can a path of densities be obtained from applying a time-dependent family of Lindbladian to an initial state? For this, we have to analyze the tangent structure of the ``manifold with corners'' and how this tangent structure reflects Lindbldian evolution. Building on this framework, we derive reachability criteria and no-go results based on a norm-decrease alignment condition, including a geometric obstruction arising from the incompatibility between admissible tangent directions and dissipative contraction.

quant-ph↗

arXiv2024

A note on the stabilizer formalism via noncommutative graphs

In this short note we formulate a stabilizer formalism in the language of noncommutative graphs. The classes of noncommutative graphs we consider are obtained via unitary representations of compact groups, and suitably chosen operators on finite-dimensional Hilbert spaces. Furthermore, in this framework, we generalize previous results in this area for determining when such noncommutative graphs have anticliques.

cs.IT↗