Entangled Rings

Abstract

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

19 pages, no figures; v2 includes new results; v3 corrects a numerical error for the case N=8

References in corpus (3)

• Three qubits can be entangled in two inequivalent ways
• Entangled webs: Tight bound for symmetric sharing of entanglement
• Entanglement molecules

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