# Toward an expected utility theory of entanglement: Optimization of a probabilistic entanglement protocol

## TL;DR

This paper develops a utility-based framework for optimizing probabilistic entanglement protocols, demonstrating that strategic choices can maximize entanglement even with weak interactions, based on a formal utility theory.

## Contribution

It introduces a utility theory for entanglement based on von Neumann--Morgenstern theorem and applies it to optimize measurement-induced entanglement protocols.

## Key findings

- Maximizing utility requires non-trivial strategies.
- Optimal strategies are especially beneficial with weak system-ancilla interactions.
- The framework guides the design of more effective probabilistic entanglement protocols.

## Abstract

A utility theory of entanglement is formulated, based on the von Neumann--Morgenstern theorem. As a specific example, a protocol for measurement--induced entanglement is studied, in which the amount of entanglement obtained depends on the random result of a measurement on an ancilla. It is shown that the maximization of the utility requires a non--trivial strategy. The results are especially useful when the interaction between the ancilla and the systems to be entangled is weak.