Measurement-Induced Randomness and Structure in
Controlled Qubit Processes

Ariadna E. Venegas-Li, Alexandra M. Jurgens, and James P. Crutchfield

Complexity Sciences Center
Physics Department
University of California at Davis
Davis, CA 95616

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.


Ariadna E. Venegas-Li, Alexandra M. Jurgens, and James P. Crutchfield, “Measurement-Induced Randomness and Structure in Controlled Qubit Processes”, Physical Review E, (2020) 040102(R).
doi:10.1103/PhysRevE.102.040102.
[pdf] 7 MB.
arxiv.org:1908.09053 [quant-ph].