All degree six local unitary invariants of k qudits

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.

18 pages, 6 figures, extended version. Comments are welcome

References in corpus (2)

• The twistor geometry of three-qubit entanglement
• Freudenthal triple classification of three-qubit entanglement

Cited by in corpus (9)

• Multipartite entanglement measures
• Partial separability revisited: Necessary and sufficient criteria
• Criterion of Local Unitary Equivalence for Multipartite States
• Stochastic Local Operations with Classical Communication of Absolutely Maximally Entangled States
• Positive maps and trace polynomials from the symmetric group
• Generalized Graph States Based on Hadamard Matrices
• The mixed two qutrit system: local unitary invariants, entanglement monotones, and the SLOCC group SL(3,C)
• Using Partial Transpose and Realignment to generate Local Unitary Invariants
• Characterization of multipartite entanglement in terms of local transformations