Abstract
We present a method to numerically calculate the dynamics driven by arbitrary Hamiltonians, in particular those with symmetry. The method enables us to study quantum state and entanglement transmission through a uniformly coupled two-dimensional square lattice with XY-type interaction. Significantly, we find that the central symmetry between sending and receiving nodes plays a crucial role in attaining maximal fidelity and entanglement transmission. In other words, the quality of a two-dimensional transmission is determined by the geometry of the nodes involved.
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