优化顶夸克-反顶夸克事件中的纠缠与贝尔不等式违背
Optimizing Entanglement and Bell Inequality Violation in Top Anti-Top Events
AI总结：
本研究解析证明使自旋关联对角化的基为最优基，可最大化顶夸克对事件中的纠缠与贝尔不等式违背，对LHC和未来正负电子对撞机实验至关重要。
摘要：
在对撞机中产生的顶夸克和反顶夸克具有关联的自旋。这些自旋构成一个量子态，可以表现出纠缠并违背贝尔不等式。在现实的对撞机实验中，大多数分析允许轴以及洛伦兹框架逐事件变化，从而引入了对事件依赖基选择的依赖性，导致我们采用“虚构态”而非真正的量子态。虚构态的基依赖性允许进行优化过程，这使得使用虚构态在测量纠缠和贝尔不等式违背方面具有优势。在这项工作中，我们解析地证明了使自旋-自旋关联对角化的基是最大化自旋关联、纠缠和贝尔不等式违背的最优基。我们表明，在$t\ar t$产生阈值附近，最优基与固定束流基（或旋转束流基）大致相同，而在远高于阈值时，它趋近于螺旋度基。使用该基，我们展示了在LHC和未来$e^+e^-$对撞机中$t\ar t$事件中纠缠和贝尔不等式违背的灵敏度。由于在实验上观察贝尔不等式违背似乎相当具有挑战性，并且在对撞机实验中需要大量数据集，选择最优基对于观察贝尔不等式违背至关重要。我们的方法和通用方法同样适用于$t\ar t$之外的其他系统，包括超出标准模型的相互作用。
英文摘要：
A top quark and an anti-top quark produced together at colliders have correlated spins. These spins constitute a quantum state that can exhibit entanglement and violate Bell's inequality. In realistic collider experiments, most analyses allow the axes, as well the Lorentz frame to vary event-by-event, thus introducing a dependence on the choice of event-dependent basis leading us to adopt "fictitious states," rather than genuine quantum states. The basis dependence of fictitious states allows for an optimization procedure, which makes the usage of fictitious states advantageous in measuring entanglement and Bell inequality violation. In this work, we show analytically that the basis which diagonalizes the spin-spin correlations is optimal for maximizing spin correlations, entanglement, and Bell inequality violation. We show that the optimal basis is approximately the same as the fixed beam basis (or the rotated beam basis) near the $t\bar t$ production threshold, while it approaches the helicity basis far above threshold. Using this basis, we present the sensitivity for entanglement and Bell inequality violation in $t\bar t$ events at the LHC and a future $e^+e^-$ collider. Since observing Bell inequality violation appears to be quite challenging experimentally, and requires a large dataset in collider experiments, choosing the optimal basis is crucially important to observe Bell inequality violation. Our method and general approach are equally applicable to other systems beyond $t \bar t$, including interactions beyond the Standard Model.
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