Related papers: The $\hbar\rightarrow 0$ Limit of the Entanglement Entropy

The $\hbar\rightarrow 0$ Limit of the Entanglement Entropy

URL: http://arxiv.org/abs/2112.06840v2
Date: Mon, 7 Mar 2022 15:54:19 GMT
Title: The $\hbar\rightarrow 0$ Limit of the Entanglement Entropy
Authors: Giuseppe Mussardo and Jacopo Viti
Abstract summary: Entangled quantum states share properties that do not have classical analogs. We show that the limit of the bipartite entanglement entropy coincides with the Shannon entropy of $N$ bits.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: Entangled quantum states share properties that do not have classical analogs, in particular, they show correlations that can violate Bell inequalities. It is therefore an interesting question to see what happens to entanglement measures -- such as the entanglement entropy for a pure state -- taking the semi-classical limit, where the naive expectation is that they may become singular or zero. This conclusion is however incorrect. In this paper, we determine the $\hbar\rightarrow 0$ limit of the bipartite entanglement entropy for a one-dimensional system of $N$ quantum particles in an external potential and we explicitly show that this limit is finite. Moreover, if the particles are fermionic, we show that the $\hbar\rightarrow 0$ limit of the bipartite entanglement entropy coincides with the Shannon entropy of $N$ bits.

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