| It is well-known that decoherence in quantum state superpositions destroys the quantumness of the system state along time. However, it is not clear how it affects the quantumness of a state along the space. How many single-spin states can one correlate through an observable many-spin quantun state superposition? This still needs to be answered. Recently, it is being shown that decoherence, induced by perturbations to a system, limits the distance over which quantum information can be transmitted. On this direction, we investigate the decoherence induced localization on many-spin quantum state superpositions in a nuclear spin-based quantum simulator. This allows us to study the size of large spin clusters that are generated by a Hamiltonian driving the transmission of information, while a variable-strength perturbation counteracts the spreading. We find that the system reaches a dynamic equilibrium size, which decreases with the square of the perturbation strength. Based on this, we show that the cluster-size evolution suffer a dynamical transition from a increasing size evolution to a decreasing size evolution depending if the initial cluster-size is lower or larger that the dynamic equilibrium size. We develop a phenomenological model to describe these results. |
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