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arXiv:2506.14721 · Journal of Physics A Mathematical and Theoretical

Large effects from quantum reference frames

Martin Bojowald A, Luis Martínez

Published Jun 19, 2025• 0 citations
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Abstract

Abstract Reference frames are used to parameterize measurements of physical effects, but since their practical realization uses material objects, they may affect observations performed in a combined quantum state of the measured system together with the frame. Here, a procedure is used that makes it possible to describe non-monotonic reference scales in a quantum treatment, revealing large quantum effects in the measured system whenever a reference frame encounters a turning point. Subtle quantum correlations in the combined state of system and frame, and more broadly the concept of relational quantum mechanics, can be tested via a characteristic and surprisingly large shift in the measured value.

DOI
10.1088/1751-8121/ade648

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Abstract Reference frames are used to parameterize measurements of physical effects, but since their practical realization uses material objects, they may affect observations performed in a combined quantum state of the measured system together with the frame. Here, a procedure is used that makes it possible to describe non-monotonic reference scales in a quantum treatment, revealing large quantum effects in the measured system whenever a reference frame encounters a turning point. Subtle quantum correlations in the combined state of system and frame, and more broadly the concept of relational quantum mechanics, can be tested via a characteristic and surprisingly large shift in the measured value.
The concept of a reference frame has been a part of the physical formalism since the early days of physics. The reference frame was always understood as a physical system with respect to which states of other physical systems are described. With the adoption of quantum theory, our understanding of physical systems has fundamentally changed, yet we still rely on classical systems for the definition of reference frames. If we acknowledge the fact that all systems are quantum mechanical, including reference frames, then we have to be able to describe quantum systems relative to other quantum systems. \n \nIn this thesis we develop a framework for integrating quantum reference frames into the formalism of quantum mechanics. We show how the description of states and measurements has to be refined in order to account for the quantum nature of the reference frame. Initially, we study the implications of the new description with a quantum reference frame associated with a generic compact group. Then, we apply the same approach to the study of relativistic quantum reference frames associated with the Poincaré group, which is not compact. \n \nOur findings for the generic compact group include an analysis of how well a quantum system defines a frame of reference for other systems. Also in the generic case we analyze the effects of a measurement on a quantum reference frame. In the relativistic case we first find how the massive representations of the Poincaré group decompose into irreducible representations. This is a key problem in the analysis of quantum reference frames. Finally, we analyze a relativistic quantum reference frame that is used for measuring the total momentum. We will show how the relativistic measurements of total momentum should be described with respect to a quantum reference frame. We will also show how these measurements affect the quantum reference frame.
Reference frames are of special importance in physics. They are usually considered to be idealized entities. However, in most situations, e.g. in laboratories, physical processes are described within reference frames constituted by physical systems. As new technological developments make it possible to demonstrate quantum properties of complex objects an interesting conceptual problem arises: Could one use states of quantum systems to define reference frames? Recently such a framework has been introduced in [F. Giacomini, E. Castro-Ruiz, and Č. Brukner, Nat Commun 10, 494 (2019)]. One of its consequences is the fact that quantum correlations depend on a physical state of an observers reference frame. The aim of this work is to examine the dynamical aspect of this phenomena and show that the same is true for correlations established during an evolution of a composite systems. Therefore, decoherence process is also relative: For some observers the reduced evolution of subsystems is unitary, whereas for others not. I also discuss implications of this results for modern developments of decoherence theory: Quantum Darwinism and Spectrum Broadcast Structures.
Viewing frames of reference as physical systems, subject to the same laws as the systems they describe, is central to the relational approach in physics. Under the assumption that quantum mechanics universally governs all physical entities, this perspective naturally leads to the concept of quantum reference frames (QRFs). We investigate the perspective-dependence of position and momentum uncertainties, correlations, covariance matrices, and entanglement within the QRF formalism. We show that the Robertson-Schrödinger uncertainty relations are frame-dependent, and so are correlations and variances, which satisfy various constraints described as inequalities. However, the determinant of the total covariance matrix, linked to the uncertainty volume in phase space, as well as variance-based entanglement criteria, remains invariant under changes of reference frame. Under specific conditions, the purities of subsystems are also invariant for different QRFs, but in general, they are perspective-dependent. These invariants suggest fundamental, robust measures of uncertainty and entanglement that persist despite changes in observational perspective, potentially inspiring dedicated quantum information protocols as well as further foundational studies.
We show that networks of quantum frames of reference, in which one frame may be used to produce multiple other frames that in their turn prepare systems which may interact with one another, have counterintuitive properties that make following the exchange of conserved quantities very subtle, and raise questions about the very nature of conserved quantities. In addition, we present an alternative approach to analysing quantum reference frames that we believe will be useful in discussions related to quantum frames of reference.
We consider the process of changing reference frames in the case where the reference frames are quantum systems. We find that, as part of this process, decoherence is necessarily induced on any quantum system described relative to these frames. We explore this process with examples involving reference frames for phase and orientation. Quantifying the effect of changing quantum reference frames provides a theoretical description for this process in quantum experiments, and serves as a first step in developing a relativity principle for theories in which all objects including reference frames are necessarily quantum.