Jordan products of quantum channels and their compatibility

dc.contributor.authorGirard, Marken
dc.contributor.authorPlávala, Martinen
dc.contributor.authorSikora, Jamieen
dc.contributor.departmentComputer Scienceen
dc.date.accessioned2021-09-03T16:37:06Zen
dc.date.available2021-09-03T16:37:06Zen
dc.date.issued2021en
dc.description.abstractGiven two quantum channels, we examine the task of determining whether they are compatible— meaning that one can perform both channels simultaneously but, in the future, choose exactly one channel whose output is desired (while forfeiting the output of the other channel). Here, we present several results concerning this task. First, we show it is equivalent to the quantum state marginal problem, i.e., every quantum state marginal problem can be recast as the compatibility of two channels, and vice versa. Second, we show that compatible measure-and-prepare channels (i.e., entanglement-breaking channels) do not necessarily have a measure-and-prepare compatibilizing channel. Third, we extend the notion of the Jordan product of matrices to quantum channels and present sufficient conditions for channel compatibility. These Jordan products and their generalizations might be of independent interest. Last, we formulate the different notions of compatibility as semidefinite programs and numerically test when families of partially dephasing-depolarizing channels are compatible.en
dc.format.mimetypeapplication/pdfen
dc.identifier.doihttps://doi.org/10.1038/s41467-021-22275-0en
dc.identifier.urihttp://hdl.handle.net/10919/104930en
dc.identifier.volume12en
dc.language.isoenen
dc.publisherNature Researchen
dc.rightsAttribution 4.0 Internationalen
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/en
dc.titleJordan products of quantum channels and their compatibilityen
dc.title.serialNature Communicationsen
dc.typeArticle - Refereeden
dc.type.dcmitypeTexten

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