Occams Quantum Strop: Synchronizing and Compressing Classical Cryptic Processes via a Quantum Channel (Open Source)
CALIFORNIA UNIV DAVIS DAVIS United States
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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.
- Statistics and Probability
- Quantum Theory and Relativity