Cardinality-Resolved Interference Accessibility in Multipartite Quantum Systems: A trace-norm framework for measurement-assisted coherence and its use in quantum hardware diagnostics

A single-qubit Ramsey or T2 measurement reports how much interference survives on a qubit, but not why the rest is missing. Phase information lost to an unobserved environment and phase information coherently redistributed into neighbouring qubits produce the same local signature, although only the second can be recovered. We study the interference that a target qubit regains when a controller measures a chosen set of helper systems and applies an outcome-dependent phase correction. For a fixed interference basis and any helper subset T, we prove that the maximum average l1 coherence recoverable this way equals 2‖C_T‖₁, twice the trace norm of the off-diagonal block of the reduced state, and that a projective measurement on T attains it. Imposing a budget on the number of helpers gives a monotone hierarchy I(0) ≤ I(1) ≤ … ≤ I(m) from local coherence to full assistance, from which we derive an access order d_η (the fewest helpers that recover a fraction η of the accessible interference) and an unlocking spectrum π_r. Exact examples show that states with identical local and fully assisted coherence can have opposite access structure, and that coherent leakage and dephasing with the same Ramsey visibility separate at the first helper layer. Exact state-vector calculations on eight qubits show the access order rising from 0.90 for depth-2 local circuits to 3.25 at depth 8 and 4.10 for Haar-random states. Applied retrospectively to published Bell-state tomography from the ibm_brisbane processor, the first layer shows that 91–96% of the accessible interference is invisible in the target marginal. We outline uses in hardware diagnostics: separating redistribution from decoherence, pairwise leakage maps from two-qubit tomography, and sizing mid-circuit readout for feed-forward. Files: the paper (PDF) and CRIA_code.zip, a Python package that regenerates every figure, table and number in the paper and numerically verifies its analytic results (run: python interference_accessibility_reproducibility.py --verify).