AI 中文总结
研究量子场论中局部运算的因果性与可实现性，对比朱布、奥克尔与费斯特、韦尔奇的方法，证明存在无法用FV方案逼近的因果通道及相关判定不可计算，同时指出一大类因果仪器FV可实现并能用于相关测量与运算逼近。
AI 中文摘要
1993年，索尔金在量子场论背景下指出，将观察者在某些时空区域可进行的操作等同于其克劳斯算子可定位的量子仪器会导致超光速通信，即所谓的索尔金悖论。朱布和奥克尔确定了量子场论仪器与爱因斯坦因果性兼容必须满足的最小条件。费斯特和韦尔奇提出了局部量子场论运算框架。本文在自由标量场的量子场论中研究这两种方法。证明存在无法通过FV方案任意良好逼近的因果通道，判定给定仪器能否通过组合多个FV运算实现是不可计算问题。但一大类因果仪器是FV可实现的，足以以非破坏方式实现任意正算符取值测量，也能以有 herald 的概率方式逼近任意量子场论运算。
英文摘要
As noted by Sorkin, regarding quantum instruments whose Kraus operators are localizable within some spacetime region as operations accessible therein leads to superluminal communication. This so-called Sorkin paradox can be resolved by further constraining the set of allowed local operations in quantum field theory (QFT). In this spirit, Fewster and Verch proposed a framework for local QFT operations that generalizes non-relativistic quantum measurement theory and does not lead to Sorkin-like paradoxes. Shortly afterwards, Jubb (and later Oeckl) identified the minimal conditions that QFT instruments must satisfy to be compatible with Einstein's causality. In this work, we study both approaches in the quantum field theory of the free scalar field. First, we prove that a very wide class of causal instruments is FV-realizable: namely, those whose measurement channels are random displacements of the field operators. As we show, this class allows implementing arbitrary instruments in a heralded, probabilistic way, as well as non-demolition measurements deterministically. Second, we construct examples of causal channels that do not admit an approximate FV realization. Some of such causal, not FV-realizable channels violate basic physical principles, so they should not be part of any measurement theory for QFT. Third, we investigate the difficulty of characterizing the set of QFT channels that can be generated through the composition of several FV schemes. In this regard, we find a countable family of simple QFT channels for which no Turing machine can discriminate between channels within or far away from the implementable set.
Comments40+25 pages, 12 figures. Minor technical corrections, updated figures, plus new abstract, introduction, discussion and conclusion. Reformulation of the undecidability theorem
