Gleason-type Theorems from Cauchy's Functional Equation

格莱森定理的简化：从布洛赫空间视角出发

Why qubits are exceptional in Gleason's theorem: a Bloch-space perspective

本文通过布洛赫空间视角简化格莱森定理，揭示二维系统中非Born概率规则的存在及高维系统中其不可能性，强调Born规则在高维下的不可避免性及量子比特的特殊性。

关于量子信息理论中的非纠缠Gleason定理

On unentangled Gleason theorems for quantum information theory

它在这里示出的Wallach的非纠缠格里森定理的加强，可以通过应用本作者的结果广义格里森定理量子多措施所产生的量子退相干泛函的调查。

经典力学中的“反Gleason”现象与同步测量

An "anti-Gleason" phenomenon and simultaneous measurements in classical mechanics

我们报道了经典力学中的一个“反格里森”现象：与量子情形相反，经典观测量的代数可以携带一个非线性准态，一个在所有由泊松-交换函数生成的子空间上都是线性的单调泛函.我们提出了一个例子，这样的准状态的情况下，相空间是2-球。这个例子是两个看似遥远的数学理论-辛拓扑和拓扑准态理论的交集。我们使用这个准状态来估计非对易哈密顿量的同时测量的误差。

Generalized Gleason theorem and finite amount of information for the context

Quantum processes cannot be reduced, in a nontrivial way, to classical processes without specifying the context in the description of a measurement procedure. This requirement is implied by the Kochen-Specker theorem in the outcome-deterministic case and, more generally, by the Gleason theorem. The latter establishes that there is only one non-contextual classical model compatible with quantum theory, the one that trivially identifies the quantum state with the classical state. However, this model requires a breaking of the unitary evolution to account for macroscopic realism. Thus, a causal c…

Gleason's theorem for composite systems

Gleason's theorem [A. Gleason, J. Math. Mech., \textbf{6}, 885 (1957)] is an important result in the foundations of quantum mechanics, where it justifies the Born rule as a mathematical consequence of the quantum formalism. Formally, it presents a key insight into the projective geometry of Hilbert spaces, showing that finitely additive measures on the projection lattice $\PH$ extend to positive linear functionals on the algebra of bounded operators $\BH$. Over many years, and by the effort of various authors, the theorem has been broadened in its scope from type I to arbitrary von Neumann alg…

自由狄拉克电子和爱因斯坦光子的量子力学以及柯西过程

Quantum mechanics of the free Dirac electrons and Einstein photons, and the Cauchy process

在凸函数空间上构造了位置坐标系下自由Dirac电子和Einstein光子方程的基本解。结果表明，这些基本解决方案是通过一个酉变换通过柯西分布在虚时间。我们研究了自由粒子的经典相对论力学是如何从自由狄拉克电子的量子力学得到的。