TY - JOUR

T1 - Covariant catalysis requires correlations and good quantum reference frames degrade little

AU - van Luijk, Lauritz

AU - Werner, Reinhard F.

AU - Wilming, Henrik

N1 - Funding Information: Acknowledgments. We would like to thank Pa-tryk Lipka-Bartosik, Victor Gitton, Nelly H. Y. Ng, Alexander Sottmeister, and Albert Werner for interesting discussions. Support by the DFG through SFB 1227 (DQ-mat), Quantum Valley Lower Saxony, and funding by the Deutsche Forschungsgemein-schaft (DFG, German Research Foundation) under Germanys Excellence Strategy EXC-2123 Quantum-Frontiers 390837967 is also acknowledged.

PY - 2023/11/6

Y1 - 2023/11/6

N2 - Catalysts are quantum systems that open up dynamical pathways between quantum states which are otherwise inaccessible under a given set of operational restrictions while, at the same time, they do not change their quantum state. We here consider the restrictions imposed by symmetries and conservation laws, where any quantum channel has to be covariant with respect to the unitary representation of a symmetry group, and present two results. First, for an exact catalyst to be useful, it has to build up correlations to either the system of interest or the degrees of freedom dilating the given process to covariant unitary dynamics. This explains why catalysts in pure states are useless. Second, if a quantum system (“reference frame”) is used to simulate to high precision unitary dynamics (which possibly violates the conservation law) on another system via a global, covariant quantum channel, then this channel can be chosen so that the reference frame is approximately catalytic. In other words, a reference frame that simulates unitary dynamics to high precision degrades only very little.

AB - Catalysts are quantum systems that open up dynamical pathways between quantum states which are otherwise inaccessible under a given set of operational restrictions while, at the same time, they do not change their quantum state. We here consider the restrictions imposed by symmetries and conservation laws, where any quantum channel has to be covariant with respect to the unitary representation of a symmetry group, and present two results. First, for an exact catalyst to be useful, it has to build up correlations to either the system of interest or the degrees of freedom dilating the given process to covariant unitary dynamics. This explains why catalysts in pure states are useless. Second, if a quantum system (“reference frame”) is used to simulate to high precision unitary dynamics (which possibly violates the conservation law) on another system via a global, covariant quantum channel, then this channel can be chosen so that the reference frame is approximately catalytic. In other words, a reference frame that simulates unitary dynamics to high precision degrades only very little.

UR - http://www.scopus.com/inward/record.url?scp=85176923110&partnerID=8YFLogxK

U2 - 10.22331/q-2023-11-06-1166

DO - 10.22331/q-2023-11-06-1166

M3 - Article

AN - SCOPUS:85176923110

VL - 7

JO - Quantum

JF - Quantum

SN - 2521-327X

M1 - 1166

ER -