Measurement-Induced Randomness and Structure in Controlled Qubit Processes

TL;DR

This paper investigates how measurements on qubits create complex classical stochastic processes that are unpredictable and require infinite features for optimal prediction, influenced by measurement choices.

Contribution

It introduces new measures of complexity for qubit measurement processes and provides algorithms for their efficient estimation, highlighting the role of nonunifilarity.

Findings

Measurement induces high unpredictability and complexity in qubit processes.

Measurement choice significantly affects the randomness and structure of the outcomes.

New quantitative measures and algorithms for complexity estimation are developed.

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.