de la Hamette Anne-Catherine, Ludescher Stefan L, Müller Markus P
Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria.
Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Vienna, Austria.
Phys Rev Lett. 2022 Dec 23;129(26):260404. doi: 10.1103/PhysRevLett.129.260404.
In the quantization of gauge theories and quantum gravity, it is crucial to treat reference frames such as rods or clocks not as idealized external classical relata, but as internal quantum subsystems. In the Page-Wootters formalism, for example, evolution of a quantum system S is described by a stationary joint state of S and a quantum clock, where time dependence of S arises from conditioning on the value of the clock. Here, we consider (possibly imperfect) internal quantum reference frames R for arbitrary compact symmetry groups, and show that there is an exact quantitative correspondence between the amount of entanglement in the invariant state on RS and the amount of asymmetry in the corresponding conditional state on S. Surprisingly, this duality holds exactly regardless of the choice of coherent state system used to condition on the reference frame. Averaging asymmetry over all conditional states, we obtain a simple representation-theoretic expression that admits the study of the quality of imperfect quantum reference frames, quantum speed limits for imperfect clocks, and typicality of asymmetry in a unified way. Our results shed light on the role of entanglement for establishing asymmetry in a fully symmetric quantum world.
在规范理论和量子引力的量子化中，至关重要的是将诸如杆或时钟之类的参考系，不作为理想化的外部经典相关物，而是作为内部量子子系统来处理。例如，在佩奇 - 伍特斯形式体系中，量子系统S的演化由S和一个量子时钟的定态联合态来描述，其中S的时间依赖性源于以时钟的值为条件。在这里，我们考虑针对任意紧致对称群的（可能不完美的）内部量子参考系R，并表明在RS上的不变态中的纠缠量与S上相应条件态中的不对称量之间存在精确的定量对应关系。令人惊讶的是，无论用于以参考系为条件的相干态系统如何选择，这种对偶性都完全成立。对所有条件态的不对称性进行平均，我们得到一个简单的表示理论表达式，它允许以统一的方式研究不完美量子参考系的质量、不完美时钟的量子速度极限以及不对称性的典型性。我们的结果揭示了纠缠在一个完全对称的量子世界中建立不对称性所起的作用。
