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A common feature of collapse models and an expected signature of thequantization of gravity at energies well below the Planck scale is thedeviation from ordinary quantum-mechanical behavior. Here, we analyse thegeneral consequences of such modifications on quantum metrology and quantumcomputing, generalizing some of the fundamental relations of quantuminformation theory. We predict a higher quantum speed limit from the newlycalculated Mandelstam-Tamm and Margolus-Levitin bounds, which in turn imply thelowering of the Heisenberg limit for parameter estimation. We explicitly derivea modified quantum Cram\'{e}r-Rao bound relating the uncertainty in determininga parameter to the inverse of the quantum Fisher information. We finallydiscuss the implications of our results on the maximum achievable speed ofquantum computation and speculate how analogue black holes could beconceptually exploited as fast quantum computers. Our results aremodel-independent and universally hold for a wide class of scenarios beyondordinary quantum mechanics.

Ultimate information bounds beyond the quantum