2023/03/01 by David Gier, James P. Crutchfield, Gier, David +1 · 1 citation
Computer Science · Mathematics · Neuroscience · Physics and Astronomy · #Algorithm #Computer science #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Independent and identically distributed random variables #Information Theory (cs.IT) #Markov process #Mathematical analysis #Mathematics #Neural dynamics and brain function #Observer (physics) #Operator (biology) #Physics #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Quantum discord #Quantum entanglement #Quantum information #Quantum mechanics #Random variable #Realization (probability) #Separable space #Separable state #Sequence (biology) #Statistical Mechanics (cond-mat.stat-mech) #Statistical physics #Statistics #Stochastic process #Theoretical computer science
paper · pdf · doi:10.48550/arxiv.2303.00162
openalex publication_date 2023/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Stationary quantum information sources emit sequences of correlated qudits -- that is, structured quantum stochastic processes. If an observer performs identical measurements on a qudit sequence, the outcomes are a realization of a classical stochastic process. We introduce quantum-information-theoretic properties for separable qudit sequences that serve as bounds on the classical information properties of subsequent measured processes. For sources driven by hidden Markov dynamics we describe how an observer can temporarily or permanently synchronize to the source's internal state using specific positive operator-valued measures or adaptive measurement protocols. We introduce a method for approximating an information source with an independent and identically-distributed, Markov, or larger memory model through tomographic reconstruction. We identify broad classes of separable processes based on their quantum information properties and the complexity of measurements required to synchronize to and accurately reconstruct them.