$n$-qubit states with maximum entanglement across all bipartitions: A graph state approach

Understand

We discuss the construction of $n$-qubit pure states with maximum bipartite entanglement across all possible choices of $k$ vs $n-k$ bi-partitioning, which implies that the Von Neumann entropy of every $k$-qubit reduced density matrix corresponding to this state should be $k \ln 2 $.

• Such states have been referred to as $k$-uniform, $k$-MM states.
• We show that a subset of the 'graph states' satisfy this condition, hence providing a recipe for constructing $k$-uniform states.
• Finding recipes for construction of $k$-uniform states using graph states is useful since every graph state can be constructed starting from a product state using only controlled-$Z$ gates.