What compels quantum measurement to violate the Bell inequalities? Suppose that regardless of measurement, one can assign to a spin-$\frac{1}{2}$ particle (qubit) a definite value of spin, called $c$-valued spin variable, but it may take any continuous real number. Suppose further that measurement maps the $c$-valued spin variable from the continuous range of possible values onto the binary standard quantum spin values $\pm 1$ while preserving the bipartite correlation. Here, we show that such $c$-valued spin variables can indeed be constructed. In this model, one may therefore argue that it is the requirement of conservation of correlation which compels quantum measurement to violate the Bell inequalities when the prepared state is entangled. We then discuss a statistical game which captures the model of measurement, wherein two parties are asked to independently map a specific ensemble of pairs of real numbers onto pairs of binary numbers $\pm 1$, under the requirement that the correlation is preserved. The conservation of correlation forces the game to respect the Bell theorem, which implies that there is a class of games no classical (i.e., local and deterministic) strategy can ever win. On the other hand, a quantum strategy with an access to an ensemble of entangled spin-$\frac{1}{2}$ particles and circuits for local quantum spin measurement can be used to win the game.

中文翻译：

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违反贝尔不等式和联合映射博弈的测量中的相关性守恒

是什么迫使量子测量违反贝尔不等式？假设无论测量如何，都可以指定自旋$\frac{1}{2}$ 粒子 (qubit) 一个确定的自旋值，称为 $C$-valued 自旋变量，但它可以取任何连续实数。进一步假设测量映射$C$-从可能值的连续范围到二进制标准量子自旋值的值自旋变量 $\pm 1$同时保持二分相关性。在这里，我们证明了这样的$C$-valued 自旋变量确实可以构造。因此，在这个模型中，人们可能会争辩说，当准备状态被纠缠时，正是相关守恒的要求迫使量子测量违反了贝尔不等式。然后，我们讨论了一个捕捉测量模型的统计游戏，其中要求两方独立地将特定的实数对集合映射到二进制数对$\pm 1$，在保持相关性的要求下。相关性守恒迫使博弈遵守贝尔定理，这意味着存在一类经典（即局部和确定性）策略无法获胜的博弈。另一方面，量子策略可以访问纠缠自旋的集合$\frac{1}{2}$ 可以使用用于局部量子自旋测量的粒子和电路来赢得比赛。