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arXiv:2401.00152

The Hamiltonian for Entangled States Cannot Be Additive

Kent A. Peacock

Published Dec 30, 2023• 0 citations
arXivHTMLPDF

Abstract

The assumption that the system Hamiltonian for entangled states is additive is widely used in orthodox quantum no-signalling arguments. It is shown that additivity implies a contradiction with the assumption that the system being studied is entangled.
DOI
10.48550/arxiv.2401.00152

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The argument of environment-assisted invariance (known as envariance) implying Born’s rule is widely used in models for quantum measurement to reason that they must yield the correct statistics, specifically for linear models. However, it has recently been shown that linear collapse models can never give rise to Born’s rule. Here, we address this apparent contradiction and point out an inconsistency in the assumptions underlying the arguments based on envariance. We use a construction in which the role of the measurement machine is made explicit and shows that the presence of envariance does not imply that every measurement will behave according to Born’s rule. Rather, it implies that every quantum state allows a measurement machine to be constructed, which yields Born’s rule when measuring that particular state. This resolves the paradox and is in agreement with the recent result of objective collapse models necessarily being nonlinear.