Fine定理的两个证明
Two Proofs of Fine's Theorem
摘要：
法恩定理涉及的问题是确定条件的问题，在这些条件下，四个二价量对的某组概率可以被认为是潜在概率分布的边缘。八个CHSH不等式是众所周知的必要条件，但Fine定理是它们也是充分条件的惊人结果。它的应用程序的问题，找到一个本地隐藏的变量理论的测量对自旋的系统在EPRB状态。在这里，我们提出了两个简单的和独立的证明精细的定理，在这个不明显的结果的起源可以很容易地看到。第一个是一个物理动机的证明，简单地说，这个匹配问题是解决使用本地隐藏变量模型给出的佩雷斯。第二个是一个简单的代数证明，它使用的概率表示的关联函数，并利用某些简化自然产生的表示。第三，不成功的尝试证明，涉及最大熵技术也简要介绍
英文摘要：
Fine's theorem concerns the question of determining the conditions under which a certain set of probabilities for pairs of four bivalent quantities may be taken to be the marginals of an underlying probability distribution. The eight CHSH inequalities are well-known to be necessary conditions, but Fine's theorem is the striking result that they are also a sufficient condition. It has application to the question of finding a local hidden variables theory for measurements of pairs of spins for a system in an EPRB state. Here we present two simple and self-contained proofs of Fine's theorem in which the origins of this non-obvious result can be easily seen. The first is a physically motivated proof which simply notes that this matching problem is solved using a local hidden variables model given by Peres. The second is a straightforward algebraic proof which uses a representation of the probabilities in terms of correlation functions and takes advantage of certain simplifications naturally arising in that representation. A third, unsuccessful attempt at a proof, involving the maximum entropy technique is also briefly described
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