Classification of nonproduct states with maximum stabilizer dimension

TL;DR

This paper characterizes nonproduct n-qubit pure states with maximum stabilizer dimensions, identifying GHZ states and their equivalents, and explores special cases like n=4 with unique stabilizer subalgebras.

Contribution

It provides a complete characterization of states with maximum stabilizer dimension, including canonical forms and Lie algebra structures, extending understanding of stabilizer subgroups in quantum states.

Findings

GHZ states have maximum stabilizer dimension for n≥3, n≠4.

For n=4, an additional maximal stabilizer subalgebra exists.

Canonical forms are provided for states with these stabilizers.

Abstract

Nonproduct n-qubit pure states with maximum dimensional stabilizer subgroups of the group of local unitary transformations are precisely the generalized n-qubit Greenberger-Horne-Zeilinger states and their local unitary equivalents, for n greater than or equal to 3 but not equal to 4. We characterize the Lie algebra of the stabilizer subgroup for these states. For n=4, there is an additional maximal stabilizer subalgebra, not local unitary equivalent to the former. We give a canonical form for states with this stabilizer as well.