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We study decoherence of propagating spin-1/2 excitations in generic(non-integrable and/or disordered) spin chains. We find the relevantdecoherence times to be shorter in both the near-critical and diffusive regimes(if any), which fact might have important implications for the recentlyproposed spin chain-based implementations of quantum information processing.Comment: Latex, 5 pages, no figure

Decoherence of one-dimensional flying qubits due to their cross-talk and imperfections