All degree six local unitary invariants of k qudits

TL;DR

This paper derives explicit, index-free formulas for all degree six local unitary invariants of k-partite quantum states, using graph-technical methods to facilitate understanding of these algebraic invariants.

Contribution

It provides the first comprehensive, explicit formulas for degree six local unitary invariants of k-qudit states, expanding the toolkit for quantum state analysis.

Findings

Explicit formulas for degree six invariants are derived.

Graph-technical methods are employed for derivation.

The approach simplifies understanding of local unitary invariants.

Abstract

We give explicit index-free formulae for all the degree six (and also degree four and two) algebraically independent local unitary invariant polynomials for finite dimensional k-partite pure and mixed quantum states. We carry out this by the use of graph-technical methods, which provides illustrations for this abstract topic.