[2607.21240] Approximate Digital Quantum Restoration

View a PDF of the paper titled Approximate Digital Quantum Restoration, by Yuan Liu and a couple of different authors

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Summary:The restoration of quantum data after subsystem loss is a central problem in quantum data processing. Nonetheless, some states stay past the attain of any restoration methods. Right here we establish the algebraic origin of digital irrecoverability, the emph{ghost data}—correlations encoded within the world state that depart no hint on any accessible subsystem. We introduce a scalar measure quantifying its magnitude and show a common error ground under which no digital restoration map can function, regardless of useful resource funding. In such circumstances solely emph{approximate} digital restoration is out there. We research the sampling value when approaching the minimal attainable restoration error, and discover it bounded when the underlying linear map displays a spectrum hole, and divergent within the gapless regime, respectively. Along with the common error ground, this dichotomy partitions all multipartite quantum states into 4 lessons. Furthermore, we present that conditional mutual data, the usual entropic diagnostic, doesn’t constrain digital recoverability. As an implication, we present that the error ground imposes a detection threshold for loss-tolerant quantum metrology.