Causal asymmetry is one of the great surprises in predictive modelling: thememory required to predictive the future differs from the memory required toretrodict the past. There is a privileged temporal direction for modelling astochastic process where memory costs are minimal. Models operating in theother direction incur an unavoidable memory overhead. Here we show that thisoverhead can vanish when quantum models are allowed. Quantum models forced torun in the less natural temporal direction not only surpass their optimalclassical counterparts, but also any classical model running in reverse time.This holds even when the memory overhead is unbounded, resulting in quantummodels with unbounded memory advantage.
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