Causal Asymmetry in a Quantum World

Abstract

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

Journal reference included, 7 pages, 4 figures plus appendices, comments welcome

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• Experimental Realization of a Quantum Autoencoder: The Compression of Qutrits via Machine Learning
• Extreme dimensionality reduction with quantum modelling
• Optimal stochastic modelling with unitary quantum dynamics
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• Matrix Product States for Quantum Stochastic Modelling
• Memory cost of temporal correlations
• Memory compression and thermal efficiency of quantum implementations of non-deterministic hidden Markov models
• Single-shot quantum memory advantage in the simulation of stochastic processes
• Memory-efficient tracking of complex temporal and symbolic dynamics with quantum simulators
• Quantum adaptive agents with efficient long-term memories
• Thermal Efficiency of Quantum Memory Compression
• Robust inference of memory structure for efficient quantum modelling of stochastic processes
• Simulating extremal temporal correlations
• Ticking-clock performance enhanced by nonclassical temporal correlations
• Quantum coarse-graining for extreme dimension reduction in modelling stochastic temporal dynamics
• Thermodynamically-Efficient Local Computation and the Inefficiency of Quantum Memory Compression
• Embedding memory-efficient stochastic simulators as quantum trajectories
• Entanglement, Complexity, and Causal Asymmetry in Quantum Theories
• Ideal stochastic process modeling with post-quantum quasiprobabilistic theories
• Quantum walks under superposition of causal order