The Resource Theoretic Paradigm of Quantum Thermodynamics with Control

Woods, Mischa P.; Horodecki, Michał

doi:10.48550/arxiv.1912.05562

Cited by 8 publications

(10 citation statements)

References 82 publications

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“…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%

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: 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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“…By applying inequalities (18) and (19) to both decompositions of Λ(ω * ) (as in the proof of Theorem 1) we conclude that inequality (31) holds with r(ε) replaced by ε ′ . Since the function…”

Section: General Resultsmentioning

confidence: 84%

“…At the same time, there are many other methods developed for getting continuity bounds for basic characteristics of finite-dimensional quantum systems: the quantum relative entropy and its generalizations [3,4,8,28,29], the Renyi and Tsallis entropy [2,6,7,30,31,32,33], the Renyi conditional entropy and its generalizations [6,11,13,34], etc. A quite universal method of getting continuity bounds was proposed and used by Hanson and Datta in [9] to obtain many new results in this directions.…”

Section: Introductionmentioning

confidence: 99%

Continuity of characteristics of composite quantum systems: a review

Shirokov¹

2022

Preprint

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General methods of quantitative and qualitative continuity analysis of characteristics of composite quantum systems are described. Several modifications of the Alicki-Fannes-Winter method are considered, which make it applicable to a wide class of characteristics in both finite-dimensional and infinite-dimensional cases. A new approximation method for obtaining local continuity conditions for various characteristics of quantum systems is proposed and described in detail. This method allows us to prove several general results (Simon-type dominated convergence theorem, the theorem about preserving continuity under convex mixtures, etc.).Uniform continuity bounds and local continuity conditions for basic characteristics of composite quantum systems are presented. Along with the results obtained earlier by different authors, a number of new results proved by the proposed methods are described.

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“…In a more operational context, quantum reference frames have also been extensively studied in quantum information theory[33][34][35][36][37][38] and quantum thermodynamics[39][40][41][42][43][44][45][46]. However, the problem of quantum frame covariance as studied here is concerned with a different class of foundational questions; see[47] for more discussion on the relation between these approaches 2.…”

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confidence: 99%

Perspective-neutral approach to quantum frame covariance for general symmetry groups

Hamette¹,

Galley²,

Hoehn³

et al. 2021

Preprint

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In the absence of external relata, internal quantum reference frames (QRFs) appear widely in the literature on quantum gravity, gauge theories and quantum foundations. Here, we extend the perspectiveneutral approach to QRF covariance to general unimodular Lie groups. This is a framework that links internal QRF perspectives via a manifestly gauge-invariant Hilbert space in the form of "quantum coordinate transformations", and we clarify how it is a quantum extension of special covariance. We model the QRF orientations as coherent states which give rise to a covariant positive operator-valued measure, furnishing a consistent probability interpretation and encompassing non-ideal QRFs whose orientations are not perfectly distinguishable. We generalize the construction of relational observables, establish a variety of their algebraic properties and equip them with a transparent conditional probability interpretation. We import the distinction between gauge transformations and physical symmetries from gauge theories and identify the latter as QRF reorientations. The "quantum coordinate maps" into an internal QRF perspective are constructed via a conditioning on the QRF's orientation, generalizing the Page-Wootters formalism and a symmetry reduction procedure to general groups. We also find two types of QRF transformations: the gauge induced "quantum coordinate transformations" as passive changes of description, which we show are always unitary, and symmetry induced active changes of relational observables from one QRF to another. We then reveal novel physical effects: (i) QRFs whose orientations admit non-trivial isotropy groups can only resolve isotropy-group-invariant properties of other subsystems; (ii) when the QRF does not admit symmetries, its internal perspective Hilbert space is not fixed and "rotates" through the kinematical subsystem Hilbert space as the QRF changes orientation. We also invoke the symmetries to extend a recent observation on the quantum relativity of subsystems to general groups, which explains the QRF dependence of entanglement and other physical properties. Finally, we compare with other approaches to QRF covariance and illustrate our findings in various examples.

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The Resource Theoretic Paradigm of Quantum Thermodynamics with Control

Cited by 8 publications

References 82 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

Continuity of characteristics of composite quantum systems: a review

Perspective-neutral approach to quantum frame covariance for general symmetry groups

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