论文标题
量子参考帧的代数特性：时间会波动吗？
Algebraic properties of quantum reference frames: Does time fluctuate?
论文作者
论文摘要
量子参考帧有望与经典参考帧有所不同，因为它们必须实现典型的量子特征，例如波动和相关性。在这里，我们表明，参考变量的波动和相关性，特别是时间的限制，受其用于参考的本质。从数学上讲，该属性是通过对系统施加约束来实现的，以确保参考变量不是物理自由度。这些约束不仅关系到参考变量以描述其行为的物理自由度，还限制了参考变量的量子波动及其与系统自由度的相关性。我们将“几乎阳性”状态的概念作为一种合适的数学方法。将其属性明确应用于最近对量子参考框架的最新兴趣的示例，这揭示了先前对可能的帧系统相互作用的限制。虽然当前讨论的时钟模型依赖于此处所示的假设使它们像量子参考框架一样一致，但放松这些假设将使模型将模型暴露于看起来相当强的新限制中。几乎阳性的国家还阐明了有关关系量子力学一致性的最近辩论。
Quantum reference frames are expected to differ from classical reference frames because they have to implement typical quantum features such as fluctuations and correlations. Here, we show that fluctuations and correlations of reference variables, in particular of time, are restricted by their very nature of being used for reference. Mathematically, this property is implemented by imposing constraints on the system to make sure that reference variables are not physical degrees of freedom. These constraints not only relate physical degrees of freedom to reference variables in order to describe their behavior, they also restrict quantum fluctuations of reference variables and their correlations with system degrees of freedom. We introduce the notion of "almost-positive" states as a suitable mathematical method. An explicit application of their properties to examples of recent interest in quantum reference frames reveals previously unrecognized restrictions on possible frame-system interactions. While currently discussed clock models rely on assumptions that, as shown here, make them consistent as quantum reference frames, relaxing these assumptions will expose the models to new restrictions that appear to be rather strong. Almost-positive states also shed some light on a recent debate about the consistency of relational quantum mechanics.
