Entanglement production by independent quantum channels

TL;DR

This paper investigates how independent quantum channels generated by certain transformations in the Hubbard model influence entanglement and the efficiency of the density-matrix renormalization group method, revealing that more channels can hinder performance.

Contribution

It introduces a transformation that creates independent quantum channels in the Hubbard model and analyzes their impact on entanglement and DMRG performance.

Findings

Quantum channels can generate entanglement similar to periodic boundary conditions.

The number and strength of channels significantly affect DMRG efficiency.

Locality of interactions alone does not improve DMRG performance.

Abstract

For the one-dimensional Hubbard model subject to periodic boundary conditions we construct a unitary transformation between basis states so that open boundary conditions apply for the transformed Hamiltonian. Despite the fact that the one-particle and two-particle interaction matrices link nearest and next-nearest neighbors only, the performance of the density-matrix renormalization group method for the transformed Hamiltonian does not improve. Some of the new interactions act as independent quantum channels which generate the same level of entanglement as periodic boundary conditions in the original formulation of the Hubbard model. We provide a detailed analysis of these channels and show that, apart from locality of the interactions, the performance of DMRG is effected significantly by the number and the strength of the quantum channels which entangle the DMRG blocks.