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.
While entanglement is known to enable exponential improvements in the sample complexity of quantum learning, it remains unclear which properties of entangled resources are responsible for such improvements. We address this question through the reduction criterion, a condition obeyed by all bound-entangled states. In $n...
This work establishes the first rigorous finite-$n bounds on quantum resource testing and hence quantum resource manipulation, thus strengthening the GQSL and providing explicit estimates on the number of copies needed to achieve a prescribed performance.
Dmitry Grinko, Ludovico Lami· arXiv.org· 0 citations
Extracting total correlations from a quantum system usually requires reconstructing its state, whereas many experiments access only a few measurement settings. A possible shortcut is to add the mutual informations obtained from complementary measurements; in dimensions above two, however, this procedure can count the s...
We introduce a measure of information loss for any quantum process that may be modeled by a prepare-evolve-measure scenario: Alice prepares an ensemble of states that gets sent via a quantum channel to Bob, who then measures the output. As a quantum channel models open system dynamics, our measure of information loss q...
James Fullwood, Wu-Zhong Guo, Bo-Yu Yang· 0 citations
This work analyzes a temporal-mode extension of the two-way LM05 quantum communication primitive, in which a message block is encoded into a fixed-weight binary occupation vector (the support) alongside classical ordering information, and derives the exact maximum-a-posteriori recovery probability.
Programmable quantum devices nominally act on a Hilbert space whose dimension grows exponentially with the number of constituents, but the presence of noise makes it unlikely that they remain coherent across all of this immense Hilbert space. Then, what is the effective coherent quantum dimension that should be associa...
Pavel Sekatski· 0 citations
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