Multipartite entanglement and quantum error identification in $D$-dimensional cluster states

Understand

An entangled state is said to be $m$-uniform if the reduced density matrix of any $m$ qubits is maximally mixed.

• This is intimately linked to pure quantum error correction codes (QECCs), which allow not only to correct errors, but also to identify their precise nature and location.
• Here, we show how to create $m$-uniform states using local gates or interactions and elucidate several QECC applications.
• We first show that $D$-dimensional cluster states are $m$-uniform with $m=2D$.