2015/08/11 by J. R. Mahoney, Mahoney, J. R., C. Aghamohammadi +3
Computer Science · Mathematics · Physics and Astronomy · #FOS: Computer and information sciences #FOS: Physical sciences #Information Theory (cs.IT) #Quantum Physics (quant-ph) #Statistical Mechanics (cond-mat.stat-mech) #cond-mat.stat-mech #cs.IT #math.IT #quant-ph
paper · pdf · doi:10.48550/arxiv.1508.02760
10 pages, 6 figures; http://csc.ucdavis.edu/~cmg/compmech/pubs/oqs.htm
arxiv created 2015/08/11 · arxiv updated 2015/08/13
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.