Alexander, R., Gvirtz-Chen, S. and Jennings, D. orcid.org/0000-0003-1201-3725 (2022) Infinitesimal reference frames suffice to determine the asymmetry properties of a quantum system. New Journal of Physics, 24 (5). 053023. ISSN 1367-2630
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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2022 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft. Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. |
Keywords: | quantum information, quantum channel theory, symmetry principles, quantum reference frames, resource theory of asymmetry |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Physics and Astronomy (Leeds) > Theoretical Physics (Leeds) |
Funding Information: | Funder Grant number EPSRC (Engineering and Physical Sciences Research Council) EP/V002732/1 Royal Society URF\R\180037 Royal Society RGF\EA\181003 |
Depositing User: | Symplectic Publications |
Date Deposited: | 17 Feb 2025 10:35 |
Last Modified: | 17 Feb 2025 10:35 |
Published Version: | https://iopscience.iop.org/article/10.1088/1367-26... |
Status: | Published |
Publisher: | IOP Publishing |
Identification Number: | 10.1088/1367-2630/ac688b |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:223362 |
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