论文标题
PT-对称和准 - 铁量子理论的操作基础
The operational foundations of PT-symmetric and quasi-Hermitian quantum theory
论文作者
论文摘要
最初提出了PT对称量子理论，目的是通过放大对哈密顿人的墓地限制来扩展标准量子理论。但是，尚未提出这种扩展，即一贯描述状态，转换，测量和组成，这是任何物理理论的要求。我们旨在回答一个问题，即与PT对称可观察物的一致物理理论是否扩展了标准量子理论。我们在一般概率理论的框架内回答了这个问题，这是物理理论的最通用框架。我们构建了由在观测值集中施加PT对称的系统的一组状态，并表明所得理论仅允许一个琐碎的状态。接下来，我们考虑了准充血性对可观察物的约束，这确保了具有不间断的PT对称性的哈密顿量下的进化单位性。我们表明，这样的系统等效于标准量子系统。最后，我们表明，如果所有可观察到的物体都是准 - 热式和PT对称，则该系统等同于实际量子系统。因此，我们的结果表明，PT对称性和准热性约束都不足以始终如一地扩展标准量子理论。
PT-symmetric quantum theory was originally proposed with the aim of extending standard quantum theory by relaxing the Hermiticity constraint on Hamiltonians. However, no such extension has been formulated that consistently describes states, transformations, measurements and composition, which is a requirement for any physical theory. We aim to answer the question of whether a consistent physical theory with PT-symmetric observables extends standard quantum theory. We answer this question within the framework of general probabilistic theories, which is the most general framework for physical theories. We construct the set of states of a system that result from imposing PT-symmetry on the set of observables, and show that the resulting theory allows only one trivial state. We next consider the constraint of quasi-Hermiticity on observables, which guarantees the unitarity of evolution under a Hamiltonian with unbroken PT-symmetry. We show that such a system is equivalent to a standard quantum system. Finally, we show that if all observables are quasi-Hermitian as well as PT-symmetric, then the system is equivalent to a real quantum system. Thus our results show that neither PT-symmetry nor quasi-Hermiticity constraints are sufficient to extend standard quantum theory consistently.
