Abstract We formulate a layer-resolved diagnostic protocol for separating different kinds of quantum-information content in a hyperentangled four-qubit state undergoing local non-Markovian pure dephasing. The protocol uses Bell-sector coherence flow as a low-cost entrance test for candidate backflow windows, but does not identify this signal with entanglement recovery. Informative windows are then promoted to local complementarity, pair-concurrence, and simultaneous all-cut negative-partial-transpose (NPT) diagnostics. For the benchmark family studied here, the pair concurrence $C_{AB}(t)$, the local complementarity defect $D_A(t)$, and the white-noise visibility threshold $v_c(t)$ of the all-cut NPT layer have closed-form expressions. These relations show explicitly that coherence backflow, bipartite entanglement recovery, local budget redistribution, and all-cut NPT activation are distinct diagnostic statements. Robustness checks under controlled-phase, visibility, reservoir-parameter, and small state-perturbation variations support the use of the hierarchy as a quantum-information decision protocol rather than as a single state measure. The result is not a new entanglement or non-Markovianity monotone; it is an operational way to decide which information layer is certified by a given measurement record and when richer reconstructions are justified.
Abstract We formulate a layer-resolved diagnostic protocol for separating different kinds of quantum-information content in a hyperentangled four-qubit state undergoing local non-Markovian pure dephasing. The protocol uses Bell-sector coherence flow as a low-cost entrance test for candidate backflow windows, but does not identify this signal with entanglement recovery. Informative windows are then promoted to local complementarity, pair-concurrence, and simultaneous all-cut negative-partial-transpose (NPT) diagnostics. For the benchmark family studied here, the pair concurrence CAB(t), the local complementarity defect DA(t), and the white-noise visibility threshold vc(t) of the all-cut NPT layer have closed-form expressions. These relations show explicitly that coherence backflow, bipartite entanglement recovery, local budget redistribution, and all-cut NPT activation are distinct diagnostic statements. Robustness checks under controlled-phase, visibility, reservoir-parameter, and small state-perturbation variations support the use of the hierarchy as a quantum-information decision protocol rather than as a single state measure. The result is not a new entanglement or non-Markovianity monotone; it is an operational way to decide which information layer is certified by a given measurement record and when richer reconstructions are justified.
Complementarity residuals quantify local-information budgets that can coincide with entanglement remainders in calibrated pure-state settings. In noisy and mixed multipartite systems, however, the same residual can remain positive even after the resource interpretation inherited from the pure-state limit is no longer justified. This preprint analyzes that change of meaning and introduces a support-layer diagnostic for complementarity residuals under mixedness. The paper separates three logical levels: the residual itself, the independent support layer, and the resource-specific interpretation that is allowed only when both are present. In the pure three-qubit calibration limit, the residual agrees with a known residual-tangle interpretation. In mixed four-qubit white-noise families, however, the residual can remain finite after the chosen all-cut NPT support layer has disappeared. A separable product-state construction further shows that local mixedness alone can generate a positive residual, so the residual is not an entanglement witness and not a genuine multipartite entanglement witness. The result is an operational hierarchy for noisy multipartite quantum states. A positive complementarity residual flags unresolved local-information budget, while independent support tests determine whether an entanglement-related interpretation is justified. The approach is intended as a safe diagnostic protocol: it preserves the usefulness of complementarity residuals while preventing overinterpretation in regimes where mixedness, local decoherence, environmental correlations, or classical mixing contribute to the observed residual.
Non-Markovian optical channels can redistribute interferometric visibility,which-path information, and entanglement in ways that are not captured byconcurrence dynamics alone. Motivated by cavity-QED, waveguide-feedback,and related photonic reservoir architectures, we study an exactly solvabletwo-qubit mini-reservoir model and interpret its reduced dynamics as an effectivelocal photonic feedback channel. For the reduced two-qubit state, predictabilityPk, visibility Vk, and concurrence C obey the mixed-state relationP2k (t)+V 2k (t)+C2(t) = Bk(t) ≤ 1, where Bk(t) is the locally accessible complementaritybudget. Within the Hilbert–Schmidt formulation of completecomplementarity, we show that the corresponding deficit is closed exactly byMk(t) ≡ 1 − Bk(t) = 2Cnlhs(t) − C2(t). The remainder therefore identifiesthe part of the nonlocal optical coherence sector that is not already encodedin concurrence. Exact trajectories for Bell, nonmaximally entangled parity,superposition-of-Bell, and Werner initial states reveal memory-inducedcollapse-and-revival structure in the accessible budget, in the visibility sectorwhen local coherence is present, and in the remainder itself. Comparisonswith one-sided discord and with the purity deficit show that Mk(t)is a distinct reduced-state diagnostic rather than a relabeling of entanglement,discord, or mixedness. Because all quantities are reconstructed fromthe same reduced two-qubit state, the framework is naturally compatible with interferometric and tomographic readout in memory-bearing quantumopticalplatforms.
Abstract Fisher information is a central diagnostic in quantum readout, sensing, and open-system dynamics, but a positive Fisher derivative is not by itself a non-Markovianity witness. This paper does not introduce a new universal monotonicity measure. Instead, it establishes an encoding-aware diagnostic rule for deciding when Fisher growth can be interpreted as information backflow and when it should be read as ordinary parameter imprinting or measurement readability. The rule separates three operational layers: input-encoded optimized Fisher geometry, channel-parameter Fisher information, and fixed-readout Fisher information. For input-encoded parameters propagated by parameter-independent CP-divisible dynamics, optimized quantum Fisher information has the expected Lyapunov contraction interpretation; a revival is therefore a genuine backflow candidate. For channel-encoded parameters, Fisher information can grow even under a Markovian semigroup because the dynamics progressively writes the process parameter into the output state. A calibrated binary readout makes the measurement layer explicit. Dephasing, amplitude-damping, and two-qubit X-state examples then show the quantum-information payoff: Fisher readability, coherence, concurrence, and complementarity coincide in special calibrated sectors but separate in general. In particular, amplitude-damped X-state slices contain regions with vanishing concurrence but nonzero phase Fisher readability. The resulting criterion is an interpretation rule, not a replacement for established non-Markovianity witnesses: Fisher growth becomes causally meaningful only after the encoding, dynamical map, and readout layer have been fixed.
Abstract Near-term quantum experiments often provide only finite-shot records of selected Pauli measurements, rather than tomographically complete data. We formulate multipartite-entanglement diagnosis as a calibrated decision problem from such records. The protocol combines binomial Pauli estimators, task-informed observable designs, score-based diagnostic models, class-conditional conformal prediction, and out-of-distribution abstention. It outputs a single label, a prediction set, or an abstention according to the available evidence. Synthetic benchmarks show genuine multipartite entanglement diagnosis up to 20 qubits and reveal an information hierarchy: global coherence probes support coarse diagnosis, whereas finer block-structure labels require richer local and few-body Pauli information.
We study complementarity dynamics in open two-qubit systems through the local budgetBA = P2A+ V 2A + C2 and its deficit DA = 1 − BA. The purpose is not to define a newnon-Markovianity measure, but to distinguish two diagnostic roles. Structure observablesdescribe how predictability, visibility, concurrence, and deficit are arranged along a statespacetrajectory, whereas flow observables record temporal recovery. Amplitude-damping anddephasing prototypes, finite parameter scans, BLP-like comparisons, and two analyticallysolvable Bell-sector results show that ΔD is mainly structural, while NC and N−D respond torevival windows. The framework therefore clarifies what complementarity budgets certify inopen two-qubit dynamics.
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).