# Energy bounds for entangled states

## TL;DR

This paper establishes energy bounds for entangled states in bipartite systems, identifies states reaching these bounds, and analyzes the likelihood of randomly generating such states, with implications for quantum technology efficiency.

## Contribution

It introduces a method to determine energy bounds for entangled bipartite states and explores their properties and generation probabilities.

## Key findings

- Energy bounds depend on entanglement levels.
- States reaching bounds are identified and characterized.
- High-energy states are rarely generated randomly in most cases.

## Abstract

We find the minimum and the maximum value for the local energy of an arbitrary finite bipartite system for any given amount of entanglement, also identifying families of states reaching these bounds and sharing formal analogies with thermal states. Then, we numerically study the probability of randomly generating pure states close to these energy bounds finding, in all the considered configurations, that it is extremely low except for the two-qubit and highly degenerate cases. These results can be important in quantum technologies to design energetically more efficient protocols.