Dressel和A. N. Jordan，J. Phys. A 45（2012）015304
Proof gap in "Sufficient conditions for uniqueness of the Weak Value" by J. Dressel and A. N. Jordan, J. Phys. A 45 (2012) 015304
摘要：
本文试图证明一个“一般定理”（GT），它给出了一个充分条件，在此条件下，一个先前引入的“一般条件平均”在最小扰动极限下唯一收敛于量子弱值。“一般条件平均”是从一个正算子值测度（POVM）中获得的，它取决于一个小的“弱点”参数g。我们指出，在“充分条件”的表述中未说明的假设使它们看起来比实际上更一般。事实上，由这些未陈述的假设加强的陈述的“充分条件”似乎非常接近于POVM算子是g中的线性多项式的假设。此外，即使假设是线性POVM，在尝试的证明中似乎也有一个关键的错误或差距。一个反例的证明GT（虽然不是其结论）。然而，我猜想，结论实际上是正确的线性POVM的上下文值选择的文章的“伪逆处方”。
英文摘要：
The article of the title attempts to prove a "General theorem" (GT) giving sufficient conditions under which a previously introduced "general conditioned average" "converges uniquely to the quantum weak value in the minimal disturbance limit." The "general conditioned average" is obtained from a positive operator valued measure (POVM) depending on a small "weakness" parameter g. We point out that unstated assumptions in the presentation of the "sufficient conditions" make them appear much more general than they actually are. Indeed, the stated "sufficient conditions" strengthened by these unstated assumptions seem very close to an assumption that the POVM operators be linear polynomials in g. Moreover, there appears to be a critical error or gap in the attempted proof, even assuming a linear POVM. A counterexample to the proof of the GT (though not to its conclusion) is given. Nevertheless, I conjecture that the conclusion is actually true for linear POVM's whose contextual values are chosen by the article's "pseudoinverse prescription".
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