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

Understand

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.