Tunnelling necessitates negative Wigner function

TL;DR

This paper explores the relationship between quantum tunnelling and non-classical probabilistic behavior using the Wigner function, establishing conditions under which tunnelling implies negativity in the Wigner function.

Contribution

It introduces a new definition of tunnelling based on the Wigner function and proves that tunnelling requires negativity in the Wigner function or the tunnelling rate operator.

Findings

Tunnelling is linked to negativity in the Wigner function.

A new criterion for tunnelling involving the tunnelling rate operator.

Negativity in the Wigner function is necessary for tunnelling to occur.

Abstract

We consider in what sense quantum tunnelling is associated with non-classical probabilistic behaviour. We use the Wigner function quasi-probability description of quantum states. We give a definition of tunnelling that allows us to say whether in a given scenario there is tunnelling or not. We prove that this can only happen if either the Wigner function is negative and/or a certain measurement operator which we call the tunnelling rate operator has a negative Wigner function.