Local unitary decomposition of tripartite arbitrary leveled qudit stabilizer states into $p$-level-qudit EPR and GHZ state

TL;DR

This paper generalizes the decomposition of tripartite stabilizer states into entangled and unentangled components for arbitrary qudit dimensions using local unitaries beyond Clifford, aiding quantum protocol design.

Contribution

It introduces a method to decompose arbitrary-level qudit stabilizer states into GHZ, EPR, and unentangled states using local unitaries beyond Clifford group.

Findings

Decomposition applies to prime-power qudit dimensions.

Algorithm characterizes entanglement via subsystem phase matrices.

Enables efficient entanglement distribution in quantum protocols.

Abstract

We study the entanglement structure of tripartite stabilizer states on $N$ qudits of dimension $D$, distributed across parties $A$, $B$, and $C$, under arbitrary local unitaries. Prior work by Bravyi et al. and Looi et al. showed that qubit and squarefree qudit stabilizer states can be transformed via local Clifford unitaries into tensor products of GHZ states, EPR pairs, and unentangled qudits [arXiv:quant-ph/0504208, arXiv:1107.1761]. We generalize this to arbitrary integer $D$ by introducing local unitaries beyond the Clifford group, enabling decomposition of prime-power qudit stabilizer states into $p$-level GHZ states, EPR pairs, and unentangled qudits. Our algorithm leverages subsystem phase matrices to characterize entanglement and applies to quantum protocols requiring efficient entanglement distribution.