# Operational symmetries of entangled states

## TL;DR

This paper investigates the special symmetries of entangled quantum states, characterizing when local operations can be equivalently realized elsewhere, and introduces a new way to quantify entanglement based on these symmetries.

## Contribution

It provides a comprehensive characterization of states with operational symmetries, including multipartite and mixed states, and links these symmetries to entanglement quantification.

## Key findings

- Identifies states with and without operational symmetries
- Develops a method to quantify entanglement via symmetries
- Connects symmetries to concepts like quantum steering and envariance

## Abstract

Quantum entanglement obscures the notion of local operations; there exist quantum states for which all local actions on one subsystem can be equivalently realized by actions on another. We characterize the states for which this fundamental property of entanglement does and does not hold, including multipartite and mixed states. Our results lead to a method for quantifying entanglement based on operational symmetries and has connections to quantum steering, envariance, the Reeh-Schlieder theorem, and classical entanglement.