Why Some Quantum States Cannot Be Recovered

Abstract:The recovery of quantum information after subsystem loss is a central challenge in quantum information processing. However, some states remain beyond the reach of any recovery strategies. Here we identify the algebraic origin of irrecoverability, the ghost information---correlations encoded in the global state that leave no trace on any accessible subsystem. We introduce a scalar measure quantifying its magnitude and prove a universal error floor below which no virtual recovery map can operate, irrespective of resource investment. We further uncover a spectral phase transition in the sampling cost: bounded when the underlying linear map exhibits a spectrum gap, and divergent with a universal exponent in the gapless regime. Together with the universal error floor, this dichotomy organizes all multipartite quantum states into four classes. Moreover, it is revealed that conditional mutual information---the standard entropic diagnostic---is fundamentally irrelevant to virtual recoverability. As an implication, we show that the error floor imposes a detection threshold for loss-tolerant quantum metrology.

arXiv:2607.21240 [quant-ph]

(or arXiv:2607.21240v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2607.21240 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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