Shuttling of spin qubits between different locations is a key element in many prospective semiconductor systems for quantum information processing, but the shuttled qubits should be protected from decoherence caused by by time- and space-dependent noise. Since the paths of different spin qubits are interrelated, the noise acting on the shuttled spins exhibits complex and unusual correlations. We appraise the role of these correlations using the concept of trajectories on random sheets, and demonstrate that they can drastically affect the efficiency of coherence protection. These correlations can be exploited to enhance the shuttling fidelity, and we show that by encoding a logical qubit in a state of two sequentially shuttled entangled spins, high fidelity can be achieved even for very slow shuttling. We identify the conditions favoring this encoding, and quantify improvement in the shuttling fidelity in comparison with single-spin shuttling. ... Read more