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arXiv · 1508.02760

Occam's Quantum Strop: Synchronizing and Compressing Classical Cryptic Processes via a Quantum Channel

J. R. Mahoney·C. Aghamohammadi·J. P. Crutchfield
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Abstract

A stochastic process's statistical complexity stands out as a fundamental property: the minimum information required to synchronize one process generator to another. How much information is required, though, when synchronizing over a quantum channel? Recent work demonstrated that representing causal similarity as quantum state-indistinguishability provides a quantum advantage. We generalize this to synchronization and offer a sequence of constructions that exploit extended causal structures, finding substantial increase of the quantum advantage. We demonstrate that maximum compression is determined by the process's cryptic order---a classical, topological property closely allied to Markov order, itself a measure of historical dependence. We introduce an efficient algorithm that computes the quantum advantage and close noting that the advantage comes at a cost---one trades off prediction for generation complexity.

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J. R. Mahoney, C. Aghamohammadi, J. P. Crutchfield. 2015-08-11. Occam's Quantum Strop: Synchronizing and Compressing Classical Cryptic Processes via a Quantum Channel. https://arxiv.org/abs/1508.02760

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