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arXiv:2211.03299

Masanes-Galley-Müller and the State-Update Postulate

Blake C. Stacey

Published Nov 7, 2022• 1 citation
arXivHTMLPDF

Abstract

Masanes, Galley and Müller claim to have derived a unique rule for quantum state update consequent upon a measurement outcome. Upon closer examination, their proof implicitly assumes its first step, namely that the state-update rule is linear.
DOI
10.48550/arxiv.2211.03299

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Masanes, Galley and Müller \cite{masanes2019measurement} argue that the measurement postulates of non-relativistic quantum mechanics follow from the structural postulates together with an assumption they call the "possibility of state estimation". Their argument also relies on what they term a "theory-independent characterization of measurements for single and multipartite systems". We refute their conclusion, giving explicit examples of non-quantum measurement and state update rules that satisfy all their assumptions. We also show that their "possibility of state estimation" assumption is neither necessary nor sufficient to ensure a sensible notion of state estimation within a theory whose states are described by the quantum formalism. We further show their purportedly "theory-independent" characterization assumes several properties of quantum measurements that exclude plausible alternative types of measurement. We illustrate all these points with specific alternative measurement postulates and post-measurement state update rules. We conclude that, contrary to some folklore, quantum mechanics is by no means an island in theory-space. It can consistently be extended by rules for obtaining information about quantum states other than via POVMs. Whether such rules are realised in nature, for example in linking quantum theory and gravity, is an empirical question that cannot be resolved by theoretical analysis alone.
Are there consistent and physically reasonable alternatives to the projection postulate? Does it have unique properties compared to acceptable alternatives? We answer these questions by systematically investigating hypothetical state-update rules for quantum systems that Nature could have chosen over the Lüders rule. Among other basic properties, any prospective rule must define unique post-measurement states and not allow for superluminal signalling. Particular attention will be paid to consistently defining post-measurement states when performing local measurements in composite systems. Explicit examples of valid unconventional update rules are presented, each resulting in a distinct, well-defined foil of quantum theory. This framework of state-update rules allows us to identify operational properties that distinguish the projective update rule from all others and to put earlier derivations of the projection postulate into perspective.
Are there consistent and physically reasonable alternatives to the projection postulate? Does it have unique properties compared with acceptable alternatives? We answer these questions by systematically investigating hypothetical state-update rules for quantum systems that Nature could have chosen over the Lüders rule. Among other basic properties, any prospective rule must define unique post-measurement states and not allow for superluminal signaling. Particular attention will be paid to consistently defining post-measurement states when performing local measurements in composite systems. Explicit examples of valid unconventional update rules are presented, each resulting in a distinct, well-defined foil of quantum theory. This framework of state-update rules allows us to identify operational properties that distinguish the projective update rule from all others and to put earlier derivations of the projection postulate into perspective.
A recent argument, attributed to Masanes, is claimed to show that the assumption that quantum measurements have definite, objective outcomes, is incompatible with quantum predictions. In this work, a detailed examination of the argument shows that it has a much narrower field of application than previously recognized. In particular, it is found: i) that the argument only applies to hidden-variable models with a particular feature; and ii) that such a feature is not present in most hidden-variable models, including pilot-wave theory. It is concluded that the argument does not succeed in calling into question the objectivity of quantum measurements.