1209.0406 (A. Carlini et al.)

Brachistochrone of Entanglement for Spin Chains    [PDF]

A. Carlini, T. Koike

We analytically investigate the time-optimal unitary evolution of entanglement between indirectly coupled qubits in a trilinear Ising chain with unequal interaction couplings. The intermediate qubit is controlled via a local magnetic field. We find the time-optimal unitary evolution law, and we quantify residual entanglement via the two-tangle between the indirectly coupled qubits, for all possible sets of initial pure quantum states of a tripartite system. The integrals of the motion of the brachistochrone are determined by fixing the minimal time at which the residual entanglement is maximized. Entanglement plays a role for $W$ and $GHZ$ initial quantum states, and for the bi-separable initial state in which the indirectly coupled qubits have a nonzero value of the 2-tangle.

View original: http://arxiv.org/abs/1209.0406