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A change of perspective: switching quantum reference frames via a perspective-neutral framework

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Augustin Vanrietvelde1, Philipp A. Hoehn1,2, Flaminia Giacomini1,2, and Esteban Castro-Ruiz1,2

1Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
2Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria

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Abstract

Treating reference frames fundamentally as quantum systems is inevitable in quantum gravity and also in quantum foundations once considering laboratories as physical systems. Both fields thereby face the question of how to describe physics relative to quantum reference systems and how the descriptions relative to different such choices are related. Here, we exploit a fruitful interplay of ideas from both fields to begin developing a unifying approach to transformations among quantum reference systems that ultimately aims at encompassing both quantum and gravitational physics. In particular, using a gravity inspired symmetry principle, which enforces physical observables to be relational and leads to an inherent redundancy in the description, we develop a perspective-neutral structure, which contains all frame perspectives at once and via which they are changed. We show that taking the perspective of a specific frame amounts to a fixing of the symmetry related redundancies in both the classical and quantum theory and that changing perspective corresponds to a symmetry transformation. We implement this using the language of constrained systems, which naturally encodes symmetries. Within a simple one-dimensional model, we recover some of the quantum frame transformations of [1], embedding them in a perspective-neutral framework. Using them, we illustrate how entanglement and classicality of an observed system depend on the quantum frame perspective. Our operational language also inspires a new interpretation of Dirac and reduced quantized theories within our model as perspective-neutral and perspectival quantum theories, respectively, and reveals the explicit link between them. In this light, we suggest a new take on the relation between a `quantum general covariance’ and the diffeomorphism symmetry in quantum gravity.

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[3] Lucien Hardy, “Implementation of the Quantum Equivalence Principle”, arXiv:1903.01289.

[4] Jianhao M. Yang, “Quantum Entanglement Induced by Mutual Gravitational Interaction”, arXiv:1903.04896.

[5] Flaminia Giacomini, Esteban Castro-Ruiz, and Časlav Brukner, “Relativistic Quantum Reference Frames: The Operational Meaning of Spin”, Physical Review Letters 123 9, 090404 (2019).

[6] Alexander R. H. Smith and Mehdi Ahmadi, “Relativistic quantum clocks observe classical and quantum time dilation”, arXiv:1904.12390.

[7] Ted Jacobson and Phuc Nguyen, “Diffeomorphism invariance and the black hole information paradox”, Physical Review D 100 4, 046002 (2019).

[8] Philipp A Hoehn and Augustin Vanrietvelde, “How to switch between relational quantum clocks”, arXiv:1810.04153.

[9] Alexander R. H. Smith, “Communicating without shared reference frames”, Physical Review A 99 5, 052315 (2019).

[10] Augustin Vanrietvelde, Philipp A Hoehn, and Flaminia Giacomini, “Switching quantum reference frames in the N-body problem and the absence of global relational perspectives”, arXiv:1809.05093.

[11] Leonardo Chataignier, “On the Construction of Quantum Dirac Observables and the Emergence of WKB Time”, arXiv:1910.02998.

[12] Veronika Baumann, Flavio Del Santo, Alexander R. H. Smith, Flaminia Giacomini, Esteban Castro-Ruiz, and Caslav Brukner, “Generalized probability rules from a timeless formulation of Wigner’s friend scenarios”, arXiv:1911.09696.

[13] Esteban Castro-Ruiz, Flaminia Giacomini, Alessio Belenchia, and Časlav Brukner, “Time reference frames and gravitating quantum clocks”, arXiv:1908.10165.

[14] Jianhao M. Yang, “Switching Quantum Reference Frames for Quantum Measurement”, arXiv:1911.04903.

[15] Philipp A. Hoehn, Alexander R. H. Smith, and Maximilian P. E. Lock, “The Trinity of Relational Quantum Dynamics”, arXiv:1912.00033.

The above citations are from SAO/NASA ADS (last updated successfully 2020-01-27 15:38:06). The list may be incomplete as not all publishers provide suitable and complete citation data.

Could not fetch Crossref cited-by data during last attempt 2020-01-27 15:38:04: Could not fetch cited-by data for 10.22331/q-2020-01-27-225 from Crossref. This is normal if the DOI was registered recently.

Source: https://quantum-journal.org/papers/q-2020-01-27-225/

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