title: Occam's Quantum Strop: Synchronizing and Compressing Classical Cryptic Processes via a Quantum Channel.
abstract: A stochastic process' 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' 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.
authors.affiliation: Complexity Sciences Center and Department of Physics, University of California at Davis, One Shields Avenue, Davis, CA 95616, USA.
authors.forename: John R
authors.initials: JR
authors.lastname: Mahoney
authors.affiliation: Complexity Sciences Center and Department of Physics, University of California at Davis, One Shields Avenue, Davis, CA 95616, USA.
authors.forename: Cina
authors.initials: C
authors.lastname: Aghamohammadi
authors.affiliation: Complexity Sciences Center and Department of Physics, University of California at Davis, One Shields Avenue, Davis, CA 95616, USA.
authors.forename: James P
authors.initials: JP
authors.lastname: Crutchfield