How many bits specify a quantum state?

TL;DR

This paper discusses the limits of precision in quantum state descriptions, proposing that finite information content per state may shed light on the quantum-classical transition.

Contribution

It introduces the idea that quantum states have finite information content, challenging the notion of infinite precision in quantum descriptions.

Findings

Finite-temperature gas example shows limits to wave function precision

Quantum states may be fundamentally discrete in information content

Implications for understanding quantum-to-classical transition

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.