Matrix permanent and quantum entanglement of permutation invariant states

TL;DR

This paper reveals a connection between the matrix permanent and quantum entanglement in permutation invariant states, enabling explicit formulas for entanglement measures using permanent inequalities.

Contribution

It establishes a novel link between matrix permanents and quantum entanglement, providing a new method to compute entanglement measures for permutation invariant states.

Findings

Permanent relates to the angle between vectors in quantum states.

Explicit formulas for geometric entanglement are derived.

The approach simplifies entanglement calculations for permutation invariant states.

Abstract

We point out that a geometric measure of quantum entanglement is related to the matrix permanent when restricted to permutation invariant states. This connection allows us to interpret the permanent as an angle between vectors. By employing a recently introduced permanent inequality by Carlen, Loss and Lieb, we can prove explicit formulas of the geometric measure for permutation invariant basis states in a simple way.