The role of correlations in a sequence of quantum observations on empirical measures

TL;DR

This paper investigates how correlations in sequences of quantum measurement outcomes affect the reconstruction of empirical distributions, using a relative entropy measure within a general quantum measurement framework.

Contribution

It introduces a relative-entropy based measure to quantify correlations in quantum measurement sequences and analyzes their impact on empirical distribution reconstruction.

Findings

Correlations significantly influence the accuracy of empirical distribution reconstruction.

The introduced measure effectively quantifies the range and impact of correlations.

Special cases like quantum jumps are also analyzed within this framework.

Abstract

The outcome of continuously measuring a quantum system is a string of data whose intricate correlation properties reflect the underlying quantum dynamics. In this paper we study the role of these correlation in reconstructing the probabilities of finite sequences of outcomes, the so-called empirical distributions. Our approach is cast in terms of generic quantum instruments, and therefore encompass all types of sequential and continuous quantum measurements. We also show how this specializes to important cases, such as quantum jumps. To quantify the precise role of correlations, we introduce a relative-entropy based measure that quantifies the range of correlations in the string, and the influence that these correlations have in reconstructing finite sequences.