Abstract: A natural question in entanglement theory is when a state ψ can be transformed into another state φ using local unitaries, measurements and classical communication. When restricting the allowed operations to the stabilizer formalism, φ is called a vertex-minor of ψ, and such vertex-minors have been well-studied in both the math and physics literature. In this talk I will show that excluding a fixed vertex-minor imposes a strong asymptotic constraint on entanglement: any sufficiently large stabilizer state ψ that does not contain a fixed but arbitrary φ as a vertex-minor must be weakly entangled (with respect to three entanglement measures). Conversely, any sufficiently large state ψ with strong entanglement must contain all sufficiently small states φ as vertex-minors.

Host: Prof. P. Eugster