CAR代数上的Markov态

Curvature-dimension conditions for symmetric quantum Markov semigroups

Following up on the recent work on lower Ricci curvature bounds for quantum systems, we introduce two noncommutative versions of curvature-dimension bounds for symmetric quantum Markov semigroups over matrix algebras. Under suitable such curvature-dimension conditions, we prove a family of dimension-dependent functional inequalities, a version of the Bonnet-Myers theorem and concavity of entropy power in the noncommutative setting. We also provide examples satisfying certain curvature-dimension conditions, including Schur multipliers over matrix algebras, Herz-Schur multipliers over group alge…

2 × 2矩阵代数上量子Markov半群的大偏差

Large deviations for quantum Markov semigroups on the 2 x 2 matrix algebra

设$({\mathcal{T}}_{*t})$是作用在全2 × 2矩阵代数上的具有吸收纯态的预对偶量子马尔可夫半群.证明了对于任意初始状态$ω$，表示状态网$({\mathcal{T}}_{*t}(ω))$的正交测度网在纯状态空间中满足大偏差原理，其速率函数以生成元的形式给出，且不依赖于$ω$ .这意味着$({\mathcal{T}}_{*t}(ω))$对所有足够大的$t$都是忠实的。研究了在弱耦合极限下出现的例子。

耗散复杂性的几何：通过李楔与不变锥实现马尔可夫量子动力学的类莱维分解定理

The Geometry of Dissipative Complexity: A Levi-Type Decomposition Theorem for Markovian Quantum Dynamics via Lie Wedges and Invariant Cones

本研究针对马尔可夫量子动力学的动力学李楔，证明了类莱维分解与重构定理，揭示了耗散在生成元几何中的编码方式，拓展了李代数结构方法至不可逆马尔可夫控制领域。

Diagonalizability of quantum Markov States on trees

We introduce quantum Markov states (QMS) in a general tree graph $G= (V, E)$, extending the Cayley tree's case. We investigate the Markov property w.r.t. the finer structure of the considered tree. The main result of this paper concerns the diagonalizability of a locally faithful QMS $φ$ on a UHF-algebra $\mathcal A_V$ over the considered tree by means of a suitable conditional expectation into a maximal abelian subalgebra. Namely, we prove the existence of a Umegaki conditional expectation $\mathfrak E : \mathcal A_V \to \mathcal D_V$ such that $$φ= φ_{\lceil \mathcal D_V}\circ \mathfrak E.$$…