Resource-based reliability of quantum-coherent devices

Abstract

Quantum devices can lose the resource needed for a specified function without entering a fixed failure subspace. We propose a resource-based reliability framework for this situation, quantifying the remaining task-relevant resource relative to a stated ideal capacity. The resource measure is selected through its operational connection to the task and the allowed operations. We develop this approach for a trusted quantum random-number generator and a calibrated two-port interferometer. Relative-entropy coherence determines the optimal asymptotic yield of standard coherent qubits under incoherent operations for the former, while logarithmic $l_1$ coherence quantifies the fringe resource of the latter and determines its calibrated correct-port probability. An exactly solvable multi-spin spin-boson model illustrates how environmental records affect these resources at the same isolated-spin dephasing strength. Collective noise preserves coherence within magnetization sectors for product inputs, but enhances the decay of Greenberger-Horne-Zeilinger branch coherence. Finite-record simulations connect the resource definitions to measurement counts and show that increasing the sample size reduces statistical fluctuations without eliminating bias from an incorrect many-spin noise model. The resulting framework provides a task-specific route to reliability assessment when a fixed failure projector is insufficient, while keeping retained resource capacity distinct from a classical survival probability.

arXiv comment18 pages, 7 figures