# Construction and universal application of entanglement erasing partner states

## TL;DR

This paper introduces entanglement erasing partner states (EEPS) that can nullify bipartite entanglement entropy in many-particle quantum states, providing a universal method to simplify entanglement calculations across different models.

## Contribution

The paper identifies EEPS that can erase entanglement entropy, revealing a universal mechanism for disentangling subspaces and enabling simplified EE computation in free and interacting models.

## Key findings

- EEPS can nullify bipartite EE in certain states
- Analytical EE results agree with numerical simulations in models
- Universal EE erasure allows efficient EE calculation in free models

## Abstract

We investigate the subadditivity of the bipartite entanglement entropy (EE) of many-particle states, represented by Slater determinants, with respect to single particle excitations. In this setting, subadditivity can be phrased as erasure of EE, i.e. as a relative decrease in EE when adding excitations to the quantum state. We identify sets of single particle states that yield zero EE if jointly excited. Such states we dub entanglement erasing partner states (EEPS). These EEPS reveal a mechanism that describes how to disentangle two subspaces of a Hilbert space by exciting additional states. We demonstrate this general finding in Anderson and many-body localized models. The studied concept of entanglement erasure further enables us to derive the EE of Slater determinants in the free tight binding model. Here, our analytical findings show surprisingly good agreement with numerical results of the interacting XXX chain. The described EEPS further impose a universal, i.e. model independent, erasure of EE for randomly excited Slater determinants. This feature allows to compute many-particle EE by means of the associated single particle states and the filling ratio. This novel finding can be employed to drastically reduce the computational effort in free models.