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Springer eBooks

On the Complexity of Measurement in Classical Physics

Edwin J Beggs, José Félix Costa, Bruno Loff, John Vivian Tucker

Published Apr 29, 2008• 14 citations
Publisher
DOI
10.1007/978-3-540-79228-4_2

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The Problem of Measurement in Quantum Mechanics

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Recently, weak measurements have attracted a lot of interest as an experimental method for the investigation of non-classical correlations between observables that cannot be measured jointly. Here, I explain how the complex valued statistics observed in weak measurements relate to the operator algebra of the conventional Hilbert space formalism and show that the algebra of operators originates from more fundamental relations between the physical properties of a quantum system that can be expressed in terms of complex conditional probabilities. In particular, commutation relations can be identified with fundamental imaginary correlations that characterize the relations between physical properties in terms of their transformation dynamics. Non-commutativity thus originates from a definition of relations between physical properties that replaces the assumption of joint reality with a complex-valued probability reflecting the dynamical response of the system to external forces, e.g. in measurement interactions.
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Quantum-classical systems exhibit a profound and often complex interplay, demanding sophisticated methodologies for analysis. This paper proposes a novel approach to quantifying the correlation between these systems – specifically, focusing on the interplay between entanglement and information flow – through a hybrid modeling framework. We present a new measure of correlation, leveraging the distinct characteristics of both quantum and classical realms, designed to capture the nuanced dynamics of this interaction. The core mechanism involves modeling the complex system using a hybrid approach, integrating quantum and classical dynamics, and subsequently developing a novel measure of correlation. This work addresses the limitations of existing methods by offering a more comprehensive and insightful understanding of this critical interplay. The exploration of this correlation will contribute to advancements in quantum information processing and fundamental physics.