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arXiv · 2601.16258

Multi-invariants in stabilizer states

Sriram Akella·Abhijit Gadde·Jay Pandey
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Abstract

Multipartite entanglement is a natural generalization of bipartite entanglement, but is relatively poorly understood. In this paper, we develop tools to calculate a class of multipartite entanglement measures - known as multi-invariants - for stabilizer states. We give an efficient numerical algorithm that computes multi-invariants for stabilizer states. For tripartite stabilizer states, we also obtain an explicit formula for any multi-invariant using the GHZ-extraction theorem. We then present a counting argument that calculates any Coxeter multi-invariant of a q-partite stabilizer state. We conjecture a closed form expression for the same. We uncover hints of an interesting connection between multi-invariants, stabilizer states and topology. We show how our formulas are further simplified for a restricted class of stabilizer states that appear as ground states of interesting models like the toric code and the X-cube model.

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Sriram Akella, Abhijit Gadde, Jay Pandey. 2026-01-22. Multi-invariants in stabilizer states. https://arxiv.org/abs/2601.16258

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