Infinite qubit rings with maximal nearest neighbor entanglement: the Bethe ansatz solution

Phys. Rev. A 73, 052326 (2006) We search for translationally invariant states of qubits on a ring that maximize the nearest neighbor entanglement. This problem was initially studied by O'Connor and Wootters [Phys. Rev. A {\bf 63}, 052302 (2001)]. We first map the problem to the search for the g...

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Bibliographic Details
Main Authors Poulsen, U. V, Meyer, T, Bruss, D, Lewenstein, M
Format Journal Article
LanguageEnglish
Published 23.12.2005
Subjects
Physics - Quantum Physics
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Summary:Phys. Rev. A 73, 052326 (2006) We search for translationally invariant states of qubits on a ring that maximize the nearest neighbor entanglement. This problem was initially studied by O'Connor and Wootters [Phys. Rev. A {\bf 63}, 052302 (2001)]. We first map the problem to the search for the ground state of a spin 1/2 Heisenberg XXZ model. Using the exact Bethe ansatz solution in the limit of an infinite ring, we prove the correctness of the assumption of O'Connor and Wootters that the state of maximal entanglement does not have any pair of neighboring spins ``down'' (or, alternatively spins ``up''). For sufficiently small fixed magnetization, however, the assumption does not hold: we identify the region of magnetizations for which the states that maximize the nearest neighbor entanglement necessarily contain pairs of neighboring spins ``down''.
DOI:10.48550/arxiv.quant-ph/0512214