Entanglement entropy and non-local duality: quantum channels and quantum
algebras
- URL: http://arxiv.org/abs/2207.12436v3
- Date: Thu, 1 Dec 2022 16:59:27 GMT
- Title: Entanglement entropy and non-local duality: quantum channels and quantum
algebras
- Authors: Oliver DeWolfe and Kenneth Higginbotham
- Abstract summary: Entanglement entropy between local spin degrees of freedom is not generically preserved by the duality.
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.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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.
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