论文标题
l $ \ ddot {u} $ der Rule，von Neumann Rule和Cirelson的Bell Chsh不平等
L$\ddot{u}$der rule, von Neumann rule and Cirelson's bound of Bell CHSH inequality
论文作者
论文摘要
在[PRL，113，050401（2014）]中，作者表明，如果采用了von Neumann投影规则，则代替L $ \ ddot {U} $ der规则，用于降低州的量化规则，而三次leggett-garg不平等的量子价值超过了它的l $ \ ddot，则超过了。这种违反l $ \ ddot {u} $ ders绑定的行为甚至可能在系统大小的渐近极限下接近不平等的代数最大值。他们还声称，对于Clauser-Horne Shimony-Holt（CHSH）的不平等，即使在Alice首先由Alice首先执行测量，也无法获得l $ \ ddot {u} $ ders BOND（称为Cirelson的Bound）。在本文中，我们已经表明，如果使用了von Neumann投影规则，则CHSH不等式的量子结合超过了Cirelson的界限，并且也可能达到其代数最大四个。因此，这对冯·诺伊曼（von Neumann）规则作为有效状态还原规则的生存能力提供了强烈的反对意见。此外，我们指出，由于实施von Neumann测量规则，通过注射额外的量子非局部性，违反了Cirelson的界限。
In [PRL, 113, 050401 (2014)] the authors have shown that instead of L$\ddot{u}$der rule, if degeneracy breaking von Neumann projection rule is adopted for state reduction, the quantum value of three-time Leggett-Garg inequality can exceed it's L$\ddot{u}$ders bound. Such violation of L$\ddot{u}$ders bound may even approach algebraic maximum of the inequality in the asymptotic limit of system size. They also claim that for Clauser-Horne-Shimony-Holt (CHSH) inequality such violation of L$\ddot{u}$ders bound (known as Cirelson's bound) cannot be obtained even when the measurement is performed sequentially first by Alice followed by Bob. In this paper, we have shown that if von Neumann projection rule is used, quantum bound of CHSH inequality exceeds it's Cirelson's bound and may also reach its algebraic maximum four. This thus provide a strong objection regarding the viability of von Neumann rule as a valid state reduction rule. Further, we pointed out that the violation of Cirelson's bound occurs due to the injection of additional quantum non-locality by the act of implementing von Neumann measurement rule.
