标题： 非结合几何和量子信息流以及弦论引力中虫洞解的R-通量变形 显示英文标题

标题： Nonassociative geometric and quantum information flows and R-flux deformations of wormhole solutions in string gravity

摘要： 本文介绍了由弦引力中的R通量变形定义的非结合几何经典和量子信息流的理论。 相应的非结合广义概念包括经典香农熵、量子冯·诺依曼熵和瑞尼熵。 根据格里戈里·佩雷尔曼对里奇流和引力理论的统计热力学方法，以及针对作为（余）切洛伦兹丛建模的相空间的广义方法，计算了基本的几何和量子信息对象。 考虑了非结合参数变形和非完整热几何版本的统计生成函数，以及它们作为密度矩阵的量子对应物，以推导熵、能量和涨落泛函。 这使我们能够定义和计算相应的经典和量子相对熵、条件熵、互信息以及非结合纠缠和热力学信息变量。 我们提出了非结合量子几何和信息流理论QGIF的原则，并研究了与修改后的引力理论相关的此类准稳态模型的基本性质。 考虑了非结合变形和纠缠的四维、4-d虫洞（由相应时空和/或动量类型坐标定义）以及八维相空间广义虫洞配置的非结合QGIF的应用。 最后，我们推测非结合量子比特、量子信道和纠缠见证者可能可穿越的相空间黑洞和虫洞；讨论了思想实验和实验室实验；并考虑了量子计算机建模和非结合几何流及引力理论测试的前景。 显示英文摘要

摘要： This article consists of an introduction to the theory of nonassociative geometric classical and quantum information flows defined by star products with R-flux deformations in string gravity. Corresponding nonassociative generalizations of the concepts of classical Shannon entropy, quantum von Neumann entropy, R\'{e}nyi entropy are formulated. The fundamental geometric and quantum information objects are computed following the Grigori Perelman statistical thermodynamic approach to Ricci flows and gravity theories generalized for phase spaces modelled as (co) tangent Lorentz bundles. Nonassociative parametric deformations and nonholonomic thermo-geometric versions of statistical generating functions, their quantum analogues as density matrices are considered for deriving the entropy, energy and fluctuation functionals. This allows us to define and compute respective classical and quantum relative and conditional entropies, mutual information and nonassociative entanglement and thermodynamic information variables. We formulate the principles of nonassociative quantum geometric and information flow theory, QGIF, and study the basic properties of such quasi-stationary models related to modified gravity theories. Applications are considered for nonassociative deformed and entangled couples of four-dimensional, 4-d, wormholes (defined by respective spacetime and/or momentum type coordinates) and nonassociative QGIFs of 8-d phase space generalized wormholes configurations. Finally, we speculate on phase space black holes and wormholes being transversable for nonassociative qubits, quantum channels and entanglement witness; thought and laboratory experiments are discussed; and perspectives for quantum computer modelling and tests of nonassociative geometric flow and gravity theories are considered.