# How much entanglement can be created in a closed system?

## TL;DR

This paper derives a tight upper bound on bipartite entanglement entropy in closed, particle-conserving quantum systems, illustrating how conservation laws limit entanglement creation and demonstrating the bound's attainability in a fermionic gas model.

## Contribution

It provides the first tight upper bound on entanglement entropy in closed systems with particle conservation and characterizes the form of maximally entangled states under these constraints.

## Key findings

- The upper bound can be reached during unitary evolution of a fermionic gas.
- Current experiments measuring Rénnyi-2 entropy are consistent with the bound.
- The bound is especially relevant for future measurements of entanglement entropy in particle-conserving systems.

## Abstract

In a closed system, the total number of particles is fixed. We ask how much does this conservation law restrict the amount of entanglement that can be created. We derive a tight upper bound on the bipartite entanglement entropy in closed systems, and find what a maximally entangled state looks like in such a system. Finally, we illustrate numerically on an isolated system of one-dimensional fermionic gas, that the upper bound can be reached during its unitary evolution, when starting in a pure state that emulates a thermal state with high enough temperature. These results are in accordance with current experiments measuring R\'enyi-2 entanglement entropy, all of which employ a particle-conserving Hamiltonian, where our bound acts as a loose bound, and will become especially important for bounding the amount of entanglement that can be spontaneously created, once a direct measurement of entanglement entropy becomes feasible.