A relational perspective on the Wigner-Araki-Yanase theorem

Loveridge, Leon

doi:10.48550/arxiv.2006.07047

Cited by 3 publications

(4 citation statements)

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“…For example, Refs. [2,7,8,[33][34][35][36]49] use standard quantum information techniques to define external relatum independent states, but also use the latter to explore to some degree the question of how a quantum state is described relative to a subsystem. However, these works do not study the relations between the different such descriptions and thus, in particular, do not study the QRF transformations.…”

Section: A Describing Physics With or Without External Relatummentioning

confidence: 99%

“…But since all physical systems are fundamentally quantum, reference frames must ultimately be quantum systems, too. This simple insight is of fundamental importance in a variety of physical fields, including quantum information theory [1][2][3][4][5][6][7][8], quantum thermodynamics [9][10][11][12][13][14][15][16][17], quantum gravity [18][19][20][21][22][23][24][25][26], and in the foundations of quantum physics [27][28][29][30][31][32][33][34][35][36][37] more generally.…”

Section: Introductionmentioning

confidence: 99%

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

Krumm,

Hoehn,

Mueller

2020

Preprint

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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.

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Section: A Describing Physics With or Without External Relatummentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Krumm,

Hoehn,

Mueller

2020

Preprint

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“…However, all physics is ultimately quantum, and thus it is crucial to realize that frames of reference are ultimately quantum systems, too. The consequences of this fundamental insight permeate several areas of physics, including quantum gravity [2][3][4][5][6][7][8][9], quantum thermodynamics [10][11][12][13][14][15][16][17][18], quantum information theory [19][20][21][22][23][24][25][26], and the foundations of quantum physics [27][28][29][30][31][32][33][34][35][36][37].…”

Section: Introductionmentioning

confidence: 99%

Internal quantum reference frames for finite Abelian groups

Hoehn

Krumm

Müller

2022

Journal of Mathematical Physics

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Employing internal quantum systems as reference frames is a crucial concept in quantum gravity, gauge theories, and quantum foundations whenever external relata are unavailable. In this work, we give a comprehensive and self-contained treatment of such quantum reference frames (QRFs) for the case when the underlying configuration space is a finite Abelian group, significantly extending our previous work [M. Krumm, P. A. Höhn, and M. P. Müller, Quantum 5, 530 (2021)]. The simplicity of this setup admits a fully rigorous quantum information–theoretic analysis, while maintaining sufficient structure for exploring many of the conceptual and structural questions also pertinent to more complicated setups. We exploit this to derive several important structures of constraint quantization with quantum information–theoretic methods and to reveal the relation between different approaches to QRF covariance. In particular, we characterize the “physical Hilbert space”—the arena of the “perspective-neutral” approach—as the maximal subspace that admits frame-independent descriptions of purifications of states. We then demonstrate the kinematical equivalence and, surprising, dynamical inequivalence of the “perspective-neutral” and the “alignability” approach to QRFs. While the former admits unitaries generating transitions between arbitrary subsystem relations, the latter, remarkably, admits no such dynamics when requiring symmetry-preservation. We illustrate these findings by example of interacting discrete particles, including how dynamics can be described “relative to one of the subystems.”

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“…One natural example arises in the presence of conserved quantities. The Wigner-Araki-Yanase (WAY) theorem [4,5,6,7,8,9] shows that conservation laws restrict the accuracy and repeatability properties of a class of quantum measurements. Also in the presence of an additive conserved quantity, Åberg [10] has shown that any unitary dynamics can be approximately realized by preparing "coherent" (thus asymmetric) states of the environment.…”

Section: Introductionmentioning

confidence: 99%

A quantum reference frame size-accuracy trade-off for quantum channels

Miyadera,

Loveridge

2020

Preprint

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The imposition of symmetry upon the nature and structure of quantum observables has recently been extensively studied, with quantum reference frames playing a crucial role. In this paper, we extend this work to quantum transformations, giving quantitative results showing, in direct analogy to the case of observables, that a "large" reference frame is required for noncovariant channels to be well approximated by covariant ones. We apply our findings to the concrete setting of SU (2) symmetry.

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A relational perspective on the Wigner-Araki-Yanase theorem

Cited by 3 publications

References 40 publications

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

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

Internal quantum reference frames for finite Abelian groups

A quantum reference frame size-accuracy trade-off for quantum channels

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