Shor-Laflamme distributions of graph states and noise robustness of entanglement

Understand

The Shor-Laflamme distribution (SLD) of a quantum state is a collection of local unitary invariants that quantify $k$-body correlations.

• We show that the SLD of graph states can be derived by solving a graph-theoretical problem.
• In this way, the mean and variance of the SLD are obtained as simple functions of efficiently computable graph properties.
• Furthermore, this formulation enables us to derive closed expressions of SLDs for some graph state families.