标题： 量子排列下的不变性排除了反统计学 显示英文标题

标题： Invariance under quantum permutations rules out parastatistics

摘要： 在粒子交换下保持不变的量子系统要么是玻色子，要么是费米子，尽管从理论上讲，量子理论可能允许在排列下出现其他类型的行为。但为什么我们在自然界中没有观察到这样的“分数量子”呢？对这个问题的分析以前主要局限于特定的量子场论模型。在这里，我们给出了两个独立的论点，从量子信息理论和关于内部量子参考系的最新研究出发，普遍排除了拟统计行为。首先，我们引入了一个完全不变性的概念：量子系统不仅应在排列下保持其局部状态，还应保持它们关于其他系统的量子信息，这类似于量子信息理论中的完全正性概念。其次，我们要求量子系统在量子排列下保持不变，即那些条件依赖于排列不变可观测量值的排列。对于这两种情况，我们证明了相应的原理只有在粒子是玻色子或费米子时才成立。我们的结果展示了量子参考系如何揭示量子物理中的一个长期问题，它们强调了量子信息组成结构的关键作用，并展示了最近提出的量子协变原理的解释力以及微妙的局限性。 显示英文摘要

摘要： Quantum systems invariant under particle exchange are either Bosons or Fermions, even though quantum theory could in principle admit further types of behavior under permutations. But why do we not observe such "paraparticles" in nature? The analysis of this question was previously limited primarily to specific quantum field theory models. Here we give two independent arguments that rule out parastatistics universally, originating in quantum information theory and recent research on internal quantum reference frames. First, we introduce a notion of complete invariance: quantum systems should not only preserve their local state under permutations, but also the quantum information that they carry about other systems, in analogy to the notion of complete positivity in quantum information theory. Second, we demand that quantum systems are invariant under quantum permutations, i.e. permutations that are conditioned on the values of permutation-invariant observables. For both, we show that the respective principle is fulfilled if and only if the particle is a Boson or Fermion. Our results show how quantum reference frames can shed light on a longstanding problem of quantum physics, they underline the crucial role played by the compositional structure of quantum information, and they demonstrate the explanatory power but also subtle limitations of recently proposed quantum covariance principles.