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Infinitesimal reference frames suffice to determine the asymmetry properties of a quantum system

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Title: Infinitesimal reference frames suffice to determine the asymmetry properties of a quantum system
Authors: Alexander, R
Gvirtz-Chen, S
Jennings, D
Item Type: Journal Article
Abstract: Symmetry principles are fundamental in physics, and while they are well understood within Lagrangian mechanics, their impact on quantum channels has a range of open questions. The theory of asymmetry grew out of information-theoretic work on entanglement and quantum reference frames, and allows us to quantify the degree to which a quantum system encodes coordinates of a symmetry group. Recently, a complete set of entropic conditions was found for asymmetry in terms of correlations relative to infinitely many quantum reference frames. However, these conditions are difficult to use in practice and their physical implications unclear. In the present theoretical work, we show that this set of conditions has extensive redundancy, and one can restrict to reference frames forming any closed surface in the state space that has the maximally mixed state in its interior. This in turn implies that asymmetry can be reduced to just a single entropic condition evaluated at the maximally mixed state. Contrary to intuition, this shows that we do not need macroscopic, classical reference frames to determine the asymmetry properties of a quantum system, but instead infinitesimally small frames suffice. Building on this analysis, we provide simple, closed conditions to estimate the minimal depolarization needed to make a given quantum state accessible under channels covariant with any given symmetry group.
Issue Date: 10-May-2022
Date of Acceptance: 20-Apr-2022
URI: http://hdl.handle.net/10044/1/96477
DOI: 10.1088/1367-2630/ac688b
ISSN: 1367-2630
Publisher: Institute of Physics (IoP) and Deutsche Physikalische Gesellschaft
Journal / Book Title: New Journal of Physics
Volume: 24
Copyright Statement: © 2022 The Author(s). Published by IOP Publishing Ltd on behalf of Deutsche Physikalische Gesellschaft and the Institute of Physics. As the Version of Record of this article is going to be/has been published on a gold open access basis under a CC BY 3.0 licence, this Accepted Manuscript is available for reuse under a CC BY 3.0 licence immediately. Although reasonable endeavours have been taken to obtain all necessary permissions from third parties to include their copyrighted content within this article, their full citation and copyright line may not be present in this Accepted Manuscript version. Before using any content from this article, please refer to the Version of Record on IOPscience once published for full citation and copyright details, as permission may be required. All third party content is fully copyright protected, and is not published on a gold open access basis under a CC BY licence, unless that is specifically stated in the figure caption in the Version of Record.
Keywords: Science & Technology
Physical Sciences
Physics, Multidisciplinary
quantum information
quantum channel theory
symmetry principles
quantum reference frames
resource theory of asymmetry
Fluids & Plasmas
02 Physical Sciences
Publication Status: Published
Article Number: ARTN 053023
Appears in Collections:Quantum Optics and Laser Science
Faculty of Natural Sciences

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