Using Partial Transpose and Realignment to generate Local Unitary Invariants

TL;DR

This paper introduces a method to generate local unitary invariants for quantum systems by linking partial transpose and realignment operations, extending the capability to systems of arbitrary dimensions.

Contribution

It establishes the equivalence of certain link transformations to partial transpose and realignment, enabling the construction of local unitary invariants for complex quantum systems.

Findings

Operators' properties are analyzed.

Implications for pure tripartite higher-dimensional states are discussed.

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.