# Minimal energy cost of entanglement extraction

## TL;DR

This paper calculates the lowest possible energy increase needed to extract entanglement from the ground state of quadratic bosonic or fermionic systems, providing a universal lower bound applicable to many physical systems.

## Contribution

It introduces a protocol-independent method to determine the minimal energy cost of entanglement extraction in quadratic systems, establishing a fundamental lower bound.

## Key findings

- Derived the minimal energy increase $\, ext{Δ}E_{ ext{min}}$ for entanglement extraction.
- Constructed modes that achieve this minimal energy cost.
- Applied results to various physical systems with examples.

## Abstract

We compute the minimal energy cost for extracting entanglement from the ground state of a bosonic or fermionic quadratic system. Specifically, we find the minimal energy increase $\Delta E_{\mathrm{min}}$ in the system resulting from replacing an entangled pair of modes, sharing entanglement entropy $\Delta S$, by a product state, and we show how to construct modes achieving this minimal energy cost. Thus, we obtain a protocol independent lower bound on the extraction of pure state entanglement from quadratic systems. Due to their generality, our results apply to a large range of physical systems, as we discuss with examples.