Title: How many bits specify a quantum state? Show Chinese title

Title: 多少位可以指定一个量子态？

Abstract: Quantum mechanics suggests that nature is discrete, with one state per phase space volume $\hbar^{3N}$. This appears to contradict the idea that the state of an N-particle system can have infinite precision and is described by a set of exponentially many complex numbers. Using a finite-temperature gas confined in a box as an example, this short paper argues that there are indeed limits to the precision of wave functions, and that this may help at understanding the quantum-to-classical transition. Show Chinese abstract

Abstract: 量子力学表明自然界是离散的，每个相空间体积$\hbar^{3N}$对应一个状态。 这似乎与这样一个观点相矛盾：N 个粒子系统的状态可以具有无限精度，并且可以用大量指数级复数来描述。 本文以有限温度下被限制在一个盒子内的气体为例，论证了波函数的精度确实存在限制，这或许有助于理解量子到经典转变的过程。