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

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

2005-12-23

arxiv.org/abs/quant-ph/0512214v3

Phys. Rev. A 73, 052326 (2006)

Physics

Quantum Physics

10 pages, 4 figures; Eq. (45) and Fig. 3 corrected, no qualitative change in conclusions

Scientific paper

10.1103/PhysRevA.73.052326

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''.

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