Entangled rings - art. no. 052302

Consider a ring of N qubits in a translationally invariant quantum state. W e ask to what extent each pair. of nearest neighbors can be entangled. Unde r certain assumptions about the form of the state, we find a formula for th e maximum possible nearest-neighbor entanglement. We then compare this maxi mum with the entanglement achieved by the ground state of an antiferromagne tic ring consisting of an even number of spin-1/2 particles. We find that, though the antiferromagnetic ground state typically does not maximize the n earest-neighbor entanglement relative to all other states, it does so relat ive to other states having zero z component of spin.