论文标题
普遍的Tsirelson从平等对称的考虑
Generalized Tsirelson's bound from parity symmetry considerations
论文作者
论文摘要
贝尔实验是一个随机游戏，具有两个二进制结果，其统计相关性由$ e_0（θ）= - \ cos（θ）$给出，其中$θ\ in [-π，π）$是一个角度输入，可以参数化游戏设置。相关函数$ e_0（θ）$属于仿射空间$ {\ cal h} \ equiv \ equiv \ left \ {e（θ）\ right \} $的所有连续且可区分的周期函数$ e（θ）$遵守均等对称性约束$ E（θ）$ e（θ）$ e（θ）= E（θ）= - θ） $ e（0）= -1 $，此外，在间隔$ [0，π）$中严格单调增加。在这里，我们展示了如何为带有两个二进制结果的随机游戏的隐藏变量明确局部统计模型，其相关函数$ e（θ）$属于仿射空间$ {\ cal H} $。这个游戏家族包括贝尔实验作为一种特殊情况。在这个随机游戏家族中，可以超出$ 2 \ sqrt {2} $的贝尔不平等，直到最大允许的代数值为4。
The Bell experiment is a random game with two binary outcomes whose statistical correlation is given by $E_0(Θ)=-\cos(Θ)$, where $Θ\in [-π, π)$ is an angular input that parameterizes the game setting. The correlation function $E_0(Θ)$ belongs to the affine space ${\cal H} \equiv \left\{E(Θ)\right\}$ of all continuous and differentiable periodic functions $E(Θ)$ that obey the parity symmetry constraints $E(-Θ)=E(Θ)$ and $E(π-Θ)=-E(Θ)$ with $E(0)=-1$ and, furthermore, are strictly monotonically increasing in the interval $[0, π)$. Here we show how to build explicitly local statistical models of hidden variables for random games with two binary outcomes whose correlation function $E(Θ)$ belongs to the affine space ${\cal H}$. This family of games includes the Bell experiment as a particular case. Within this family of random games, the Bell inequality can be violated beyond the Tsirelson bound of $2\sqrt{2}$ up to the maximally allowed algebraic value of 4. In fact, we show that the amount of violation of the Bell inequality is a purely geometric feature.
