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Tunnelling necessitates negative Wigner function

In quantum tunnelling, a particle tunnels through a barrier that it classically could not surmount.

Physical Review Letters (2016)

Y. Lin, O. Dahlsten

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• Arxiv

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.