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arXiv:2107.03513

Qubits are not observers -- a no-go theorem

Časlav Brukner

Published Jul 7, 2021• 57 citations
arXivHTMLPDF

Abstract

The relational approach to quantum states asserts that the physical description of quantum systems is always relative to something or someone. In relational quantum mechanics (RQM) it is relative to other quantum systems, in the (neo-)Copenhagen interpretation of quantum theory to measurement contexts, and in QBism to the beliefs of the agents. In contrast to the other two interpretations, in RQM any interaction between two quantum systems counts as a "measurement", and the terms "observer" and "observed system" apply to arbitrary systems. We show, in the form of a no-go theorem, that in RQM the physical description of a system relative to an observer cannot represent knowledge about the observer in the conventional sense of this term. The problem lies in the ambiguity in the choice of the basis with respect to which the relative states are to be defined in RQM. In interpretations of quantum theory where observations play a fundamental role, the problem does not arise because the experimental context defines a preferred basis.

DOI
10.48550/arxiv.2107.03513

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The relational approach to quantum states asserts that the physical description of quantum systems is always relative to something or someone. In relational quantum mechanics (RQM) it is relative to other quantum systems, in the (neo-)Copenhagen interpretation of quantum theory to measurement contexts, and in QBism to the beliefs of the agents. In contrast to the other two interpretations, in RQM any interaction between two quantum systems counts as a "measurement", and the terms "observer" and "observed system" apply to arbitrary systems. We show, in the form of a no-go theorem, that in RQM the physical description of a system relative to an observer cannot represent knowledge about the observer in the conventional sense of this term. The problem lies in the ambiguity in the choice of the basis with respect to which the relative states are to be defined in RQM. In interpretations of quantum theory where observations play a fundamental role, the problem does not arise because the experimental context defines a preferred basis.
Relational quantum mechanics (RQM) is an interpretation of quantum mechanics based on the idea that quantum states do not describe an absolute property of a system but rather a relationship between systems. There have recently been some criticisms of RQM pertaining to issues around intersubjectivity. In this article, we show how RQM can address these criticisms by adding a new postulate which requires that all of the information possessed by a certain observer is stored in physical variables of that observer and thus is accessible by measurement to other observers. This makes it possible for observers to reach intersubjective agreement about quantum events that have occurred in the past. We suggest a possible ontology for a version of RQM employing this postulate; this ontology upholds the principle that quantum states are always relational, but it also postulates a set of quantum events that are not strictly relational. We show that the new postulate helps address the preferred basis problem in RQM.
Relational quantum mechanics (RQM) purportedly resolves the measurement problem by the postulate that physical variables can take determinate values that are relational in the sense that they are indexed to particular systems. Physical variables take on relational definite values if and only if two systems interact. The discrete nature of interactions required creates an ambiguity as to whether quantum events take place in the context of weak and continuous measurements and interactions. We provide a careful analysis of this problem, explain what a full solution to this problem would require, and then analyse certain proposed resolutions - finding all of them to be insufficient in their present form. Since ‘interactions’ (and the quantum events they underpin) are central to all versions of RQM, no version of RQM presented in the literature so far resolves the measurement problem.
Quantum mechanics reveals that physical quantities and informational states are not absolute but relational, depending on the context of interaction between systems. While classical physics already contained relational elements—most clearly in Galilean relativity and Einstein’s relational spacetime—the quantum domain extends relationality to physical properties and facts themselves. In this paper, I develop an info-computational perspective on relational quantum mechanics (RQM), conceiving observers as informational agents embedded within physical processes. Quantum states are understood as constraints on possible interactions rather than intrinsic attributes of isolated systems. I review key relational, perspectival, and information-theoretic approaches—including QBism, perspectival quantum realism, reference-frame–dependent observables, categorical quantum mechanics, and graph-based formalisms—and argue that they converge on a view of physics grounded in relations and information flow. Relational objectivity emerges through inter-agent translation rules rather than observer independence, providing a unified framework for understanding quantum measurement, inter-observer agreement, and physical ontology.
Abstract This paper develops an agent-centric account of measurement that treats the preferred-basis problem as fundamentally perspectival. On this view, the system–apparatus–environment decomposition and the observables that are apt to become classically robust are determined by the physical constitution and epistemic constraints of an embodied class of agents. Decoherence then stabilises those agent-specified observables, yielding facts that are stable for us without positing an absolute, observer-independent basis. On this picture, ‘measurements’ are public not because they are metaphysically privileged, but because agents like us share the relevant sensorimotor and operational structure. I motivate this account through a discussion of two recent no-go results for relational quantum mechanics (RQM) [1, 2], and a subsequent response [3]: my aim is not to defend RQM per se, but to refine the relational insight with a principled account of basis selection rooted in embodiment. I provide a phenomenological gloss, drawing on body-schema considerations, to argue that quantum mechanics is best understood as an idiosyncratically human description of interactions with the physical world—a structurally constrained, agent-indexed framework within which classicality emerges.
Relational Quantum Mechanics (RQM) claims to be an interpretation of quantum theory \cite{Rovelli.21}. However, there are significant departures from quantum theory: (i) in RQM measurement outcomes arise from interactions which entangle a system S and an observer A without decoherence, and (ii) such an outcome is a "fact" relative to the observer A , but it is not a fact relative to another observer B who has not interacted with S or A during the foregoing measurement process. For B the system S⊗A remains entangled. We derive a GHZ-like contradiction showing that relative facts described by these statements are incompatible with quantum theory. Hence Relational Quantum Mechanics should not be considered an interpretation of quantum theory, according to a criterion for interpretations that we have introduced. The criterion states that whenever an interpretation introduces a notion of outcomes, these outcomes, whatever they are, must follow the probability distribution specified by the Born rule.
Rovelli’s RQM is first characterized by contrast with both Everett’s and Bohr’s interpretations of quantum mechanics. Then, it is shown that a basic difficulty arises from the choice of formulating RQM in a naturalistic framework. Even though, according to Rovelli’s interpretation, statements about the world only make sense relative to certain naturalized observers described by means of quantum mechanics, this very meta-statement seems to make sense relative to a sort of super-observer which does not partake of the naturalized status of ordinary observers. The difficulty is solved by substituting functional reference frames for physical (or naturalized) observers throughout. Instead of being relative to physical observers, statements about the state vector of physical systems are here relative to well-defined projects of probabilistic prediction which may be embodied by several physical observers.