Why Some Quantum States Cannot Be Recovered

• URL: http://arxiv.org/abs/2607.21240v1
• Date: Thu, 23 Jul 2026 11:58:01 GMT
• Title: Why Some Quantum States Cannot Be Recovered
• Abstract summary: We identify the origin of irrecoverability, the ghost information, encoded in the global state that leave no trace on any subsystem.<n>We show that the error floor imposes a detection threshold for loss-tolerant quantum metrology.
• Score: 3.722125357019147
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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