Coherence and Asymmetry Cannot be Broadcast

Physical Review Letters
Matteo Lostaglio, Markus P Müller

Abstract

In the presence of conservation laws, superpositions of eigenstates of the corresponding conserved quantities cannot be generated by quantum dynamics. Thus, any such coherence represents a potentially valuable resource of asymmetry, which can be used, for example, to enhance the precision of quantum metrology or to enable state transitions in quantum thermodynamics. Here we ask if such superpositions, already present in a reference system, can be broadcast to other systems, thereby distributing asymmetry indefinitely at the expense of creating correlations. We prove a no-go theorem showing that this is forbidden by quantum mechanics in every finite-dimensional system. In doing so, we also answer some open questions in the quantum information literature concerning the sharing of timing information of a clock and the possibility of catalysis in quantum thermodynamics. We also prove that even weaker forms of broadcasting, of which Åberg's "catalytic coherence" is a particular example, can only occur in the presence of infinite-dimensional reference systems. Our results set fundamental limits on the creation and manipulation of quantum coherence and shed light on the possibilities and limitations of quantum reference frames to act ...Continue Reading

References

Apr 8, 1996·Physical Review Letters·H BarnumB Schumacher
Mar 21, 2008·Physical Review Letters·Marco PianiRyszard Horodecki
Jun 27, 2013·Nature Communications·Michał Horodecki, Jonathan Oppenheim
May 14, 2014·Nature Communications·Iman Marvian, Robert W Spekkens
Nov 7, 2014·Physical Review Letters·Johan Åberg
Feb 13, 2015·Proceedings of the National Academy of Sciences of the United States of America·Fernando BrandãoStephanie Wehner
Mar 11, 2015·Nature Communications·Matteo LostaglioTerry Rudolph
Apr 2, 2016·Physical Review Letters·Michał OszmaniecAntoni Wójcik

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Citations

Jan 11, 2020·Physical Review Letters·Philippe FaistFernando G S L Brandão
Sep 24, 2019·Reports on Progress in Physics·Matteo Lostaglio
Dec 5, 2020·Physical Review Letters·Li-Chao PengJian-Wei Pan
May 1, 2021·Physical Review Letters·Naoto Shiraishi, Takahiro Sagawa

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