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

• URL: http://arxiv.org/abs/2411.08214v1
• Date: Tue, 12 Nov 2024 22:09:32 GMT
• Title: The role of correlations in a sequence of quantum observations on empirical measures
• Authors: Joseph A. Smiga, Gabriel T. Landi,
• Abstract summary: We study the role of correlation in reconstructing the probabilities of finite sequences of outcomes. Our approach is cast in terms of generic quantum instruments, and therefore encompass all types of sequential and continuous quantum measurements.
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• 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.

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