Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1007.2292 · Journal of Physics A Mathematical and Theoretical

Physics within a quantum reference frame

R. M. Angelo, Nicolas Brunner, Sandu Popescu, Anthony J. Short, Paul Skrzypczyk

Published Mar 10, 2011• 96 citations
arXivHTMLPDF

Abstract

We investigate the physics of quantum reference frames. Specifically, we study several simple scenarios involving a small number of quantum particles, whereby we promote one of these particles to the role of a quantum observer and ask what is the description of the rest of the system, as seen by this observer? We highlight the interesting aspects of such questions by presenting a number of apparent paradoxes. By unravelling these paradoxes, we obtain a better understanding of the physics of quantum reference frames.

DOI
10.1088/1751-8113/44/14/145304

Related papers

Quantum frames of reference

Yakir Aharonov, T. Kaufherr

Frames of reference attached to quantum-mechanical objects of finite mass are considered. A consistent discription of such frames is obtained which resolves a variety of apparent paradoxes associated with such a description. The main result of the present work is a formalism wherein the principle of equivalence is extended to reference frames described by quantum states.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Jul 15, 1984•193 citations

A paradox in quantum measurement theory

Andrew Holster

This paper outlines a ‘paradox’ in quantum measurement theory, illustrated with two different types of systems. If this paradox cannot be resolved in ordinary quantum mechanics (as I currently think), it is alarming. If it can be resolved, it can be added to a long list of examples that show the internal consistency of quantum mechanics, and in this case I hope the correct analysis will be an interesting example for students. The immediate paradox involves a failure of Lorentz invariance for measurements on certain types of single particle systems. It seems to show that an absolute frame of reference is required to describe wave function collapse. But if the argument is correct, quantum measurement theory is not merely dependant on the frame of collapse - it is inconsistent, and experimental tests would have to be done to verify whether the apparent non-local effects predicted are real.

•Mar 1, 2004•0 citations

Particle mixing and quantum reference frames

Antonio Capolupo, Gabriele Pisacane, Aniello Quaranta

We discuss the role of quantum reference frames in providing a viable definition of rest frame for mixed particles. We then analyze the related concept of frame-dependent entanglement and its impact on the phenomenology of neutral mesons and neutrinos.

arXiv:2601.08898•Jan 13, 2026•0 citations

An Operational Resolution of the Third-Particle Paradox

Časlav Brukner, Esteban Castro-Ruiz, Marius Krumm

We give an operational resolution of the third-particle paradox, relevant in the theory of quantum reference frames. The apparent paradox is that a system which is irrelevant in one quantum-reference-frame description can seem to become relevant after changing to another quantum reference frame, because the reduced state obtained after transforming a larger system need not agree with the state obtained by first discarding the extra system and then transforming. We argue that this comparison is not operationally meaningful unless the observables are transformed together with the states, or equivalently, unless the subsystem that needs to be discarded is properly identified. If the third particle is irrelevant for all measurements actually available in the original frame, then the transformed measurements form a restricted algebra in the new frame for which the third particle remains irrelevant. The paradox therefore results from replacing an operational statement about probabilities by a stronger, representation-dependent statement about equality of reduced density operators. We close by relating the question of when degrees of freedom may be discarded to the observable-induced, operational approach to subsystem structure.

quant-pharXiv:2607.20815•Jul 24, 2026•0 citations

Networks of quantum reference frames and the nature of conserved quantities

Daniel Collins, Carolina Moreira Ferrera, Ismael L. Paiva +1 more

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.

quant-pharXiv:2603.25485•Mar 27, 2026•0 citations

Quantum reference frame transformations as symmetries and the paradox of the third particle

Marius Krumm, Philipp A. Höhn, Markus P. Müller

In a quantum world, reference frames are ultimately quantum systems too – but what does it mean to "jump into the perspective of a quantum particle"? In this work, we show that quantum reference frame (QRF) transformations appear naturally as symmetries of simple physical systems. This allows us to rederive and generalize known QRF transformations within an alternative, operationally transparent framework, and to shed new light on their structure and interpretation. We give an explicit description of the observables that are measurable by agents constrained by such quantum symmetries, and apply our results to a puzzle known as the `paradox of the third particle'. We argue that it can be reduced to the question of how to relationally embed fewer into more particles, and give a thorough physical and algebraic analysis of this question. This leads us to a generalization of the partial trace (`relational trace') which arguably resolves the paradox, and it uncovers important structures of constraint quantization within a simple quantum information setting, such as relational observables which are key in this resolution. While we restrict our attention to finite Abelian groups for transparency and mathematical rigor, the intuitive physical appeal of our results makes us expect that they remain valid in more general situations.

arXiv:2011.01951•Quantum•Aug 27, 2021•50 citations
We investigate the physics of quantum reference frames. Specifically, we study several simple scenarios involving a small number of quantum particles, whereby we promote one of these particles to the role of a quantum observer and ask what is the description of the rest of the system, as seen by this observer? We highlight the interesting aspects of such questions by presenting a number of apparent paradoxes. By unravelling these paradoxes, we obtain a better understanding of the physics of quantum reference frames.
This paper outlines a ‘paradox’ in quantum measurement theory, illustrated with two different types of systems. If this paradox cannot be resolved in ordinary quantum mechanics (as I currently think), it is alarming. If it can be resolved, it can be added to a long list of examples that show the internal consistency of quantum mechanics, and in this case I hope the correct analysis will be an interesting example for students. The immediate paradox involves a failure of Lorentz invariance for measurements on certain types of single particle systems. It seems to show that an absolute frame of reference is required to describe wave function collapse. But if the argument is correct, quantum measurement theory is not merely dependant on the frame of collapse - it is inconsistent, and experimental tests would have to be done to verify whether the apparent non-local effects predicted are real.
We give an operational resolution of the third-particle paradox, relevant in the theory of quantum reference frames. The apparent paradox is that a system which is irrelevant in one quantum-reference-frame description can seem to become relevant after changing to another quantum reference frame, because the reduced state obtained after transforming a larger system need not agree with the state obtained by first discarding the extra system and then transforming. We argue that this comparison is not operationally meaningful unless the observables are transformed together with the states, or equivalently, unless the subsystem that needs to be discarded is properly identified. If the third particle is irrelevant for all measurements actually available in the original frame, then the transformed measurements form a restricted algebra in the new frame for which the third particle remains irrelevant. The paradox therefore results from replacing an operational statement about probabilities by a stronger, representation-dependent statement about equality of reduced density operators. We close by relating the question of when degrees of freedom may be discarded to the observable-induced, operational approach to subsystem structure.
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.
In a quantum world, reference frames are ultimately quantum systems too – but what does it mean to "jump into the perspective of a quantum particle"? In this work, we show that quantum reference frame (QRF) transformations appear naturally as symmetries of simple physical systems. This allows us to rederive and generalize known QRF transformations within an alternative, operationally transparent framework, and to shed new light on their structure and interpretation. We give an explicit description of the observables that are measurable by agents constrained by such quantum symmetries, and apply our results to a puzzle known as the `paradox of the third particle'. We argue that it can be reduced to the question of how to relationally embed fewer into more particles, and give a thorough physical and algebraic analysis of this question. This leads us to a generalization of the partial trace (`relational trace') which arguably resolves the paradox, and it uncovers important structures of constraint quantization within a simple quantum information setting, such as relational observables which are key in this resolution. While we restrict our attention to finite Abelian groups for transparency and mathematical rigor, the intuitive physical appeal of our results makes us expect that they remain valid in more general situations.