Using Partial Transpose and Realignment to generate Local Unitary Invariants

Abstract

Motivated by link transformations of lattice gauge theory, a method for generating local unitary invariants, especially for a system of qubits, has been pointed out in an earlier work [M. S. Williamson {\it et. al.}, Phys. Rev. A {\bf 83}, 062308 (2011)]. This paper first points the equivalence of the so constructed transformations to the combined operations of partial transpose and realignment. This allows construction of local unitary invariants of any system, with subsystems of arbitrary dimensions. Some properties of the resulting operators and consequences for pure tripartite higher dimensional states are briefly discussed.

5 pages, 2 figures

References in corpus (1)

• All entangled states are useful for channel discrimination

Cited by in corpus (5)

• Diagonal unitary entangling gates and contradiagonal quantum states
• Partial transpose criteria for symmetric states
• Criterion of Local Unitary Equivalence for Multipartite States
• Simple permutation-based measure of quantum correlations and maximally-3-tangled states
• Local Unitary Invariants for Multipartite Quantum Systems