Measurement-Induced Randomness and Structure in Controlled Qubit Processes

Abstract

When an experimentalist measures a time series of qubits, the outcomes generate a classical stochastic process. We show that measurement induces high complexity in these processes in two specific senses: they are inherently unpredictable (positive Shannon entropy rate) and they require an infinite number of features for optimal prediction (divergent statistical complexity). We identify nonunifilarity as the mechanism underlying the resulting complexities and examine the influence that measurement choice has on the randomness and structure of measured qubit processes. We introduce new quantitative measures of this complexity and provide efficient algorithms for their estimation.

arXiv comment6 pages, 3 figures; supplemental material, 5 pages, 1 figure; http://csc.ucdavis.edu/~cmg/compmech/pubs/qdic_prl.htm

References in corpus (15)

• Quantum metrology
• Non-Markovian quantum processes: complete framework and efficient characterisation
• Ultrafast spin-lasers
• Experimental neural network enhanced quantum tomography
• Occam's Quantum Razor: How Quantum Mechanics can reduce the complexity of classical models
• Anatomy of a Bit: Information in a Time Series Observation
• Practical Bayesian Tomography
• Prediction, Retrodiction, and The Amount of Information Stored in the Present
• Hidden Markov models for stochastic thermodynamics
• Scalable reconstruction of unitary processes and Hamiltonians
• A Closed-Form Shave from Occam's Quantum Razor: Exact Results for Quantum Compression
• Bootstrapping quantum process tomography via a perturbative ansatz
• Guaranteed recovery of quantum processes from few measurements
• Nearly Maximally Predictive Features and Their Dimensions
• Strong and Weak Optimizations in Classical and Quantum Models of Stochastic Processes

Cited by in corpus (5)

• Shannon Entropy Rate of Hidden Markov Processes
• Divergent Predictive States: The Statistical Complexity Dimension of Stationary, Ergodic Hidden Markov Processes
• Fraudulent White Noise: Flat power spectra belie arbitrarily complex processes
• Ambiguity Rate of Hidden Markov Processes
• Engines for predictive work extraction from memoryful quantum stochastic processes