The quantum symmetric simple exclusion process (Q-SSEP) is a model for quantum stochastic dynamics of fermions hopping along the edges of a graph with Brownian noisy amplitudes and driven out-of-equilibrium by injection-extraction processes at a few vertices. We present a solution for the invariant probability measure of the one dimensional Q-SSEP in the infinite size limit by constructing the steady correlation functions of the system density matrix and quantum expectation values. These correlation functions code for a rich structure of fluctuating quantum correlations and coherences. Although our construction does not rely on the standard techniques from the theory of integrable systems, it is based on a remarkable interplay between the permutation groups and polynomials. We incidentally point out a possible combinatorial interpretation of the Q-SSEP correlation functions via a surprising connexion with geometric combinatorics and the associahedron polytopes.

量子对称简单排除过程（Q-SSEP）是一个费米子的量子随机动力学模型，该费米子具有布朗噪声幅度，沿着图的边缘跳动，并通过注入提取过程在几个顶点上驱使失衡。通过构造系统密度矩阵和量子期望值的稳态相关函数，我们提出了在无限大小限制下一维Q-SSEP不变概率测度的解决方案。这些相关函数编码了波动的量子相关性和相干性的丰富结构。尽管我们的构造不依赖可积系统理论的标准技术，但它是基于置换组和多项式之间的显着相互作用。