Entanglement entropy and non-local duality: quantum channels and quantum algebras

TL;DR

This paper explores how entanglement entropy transforms under dualities in quantum systems, revealing that local entanglement is transferred to non-local degrees of freedom rather than lost, using quantum channels and algebraic methods.

Contribution

It introduces a duality framework analyzing entanglement transformation, combining quantum channel and algebraic approaches to show entanglement transfer to non-local degrees of freedom.

Findings

Entanglement entropy is not preserved locally under duality.

Entanglement is transferred to non-local degrees of freedom.

Duality preserves total entanglement, just redistributes it.

Abstract

We investigate the transformation of entanglement entropy under dualities, using the Kramers-Wannier duality present in the transverse field Ising model as our example. Entanglement entropy between local spin degrees of freedom is not generically preserved by the duality; instead, entangled states may be mapped to states with no local entanglement. To understand the fate of this entanglement, we consider two quantitative descriptions of degrees of freedom and their transformation under duality. The first involves Kraus operators implementing the partial trace as a quantum channel, while the second utilizes the algebraic approach to quantum mechanics, where degrees of freedom are encoded in subalgebras. Using both approaches, we show that entanglement of local degrees of freedom is not lost; instead it is transferred to non-local degrees of freedom by the duality transformation.