Inference is a versatile tool that underlies scientific discovery, machine learning, and everyday decision-making: it describes how an agent updates a probability distribution as partial information is acquired from multiple measurements, reducing ignorance about a system's latent state. We define an inferential efficiency as the ratio of information gain to cumulative memory erasure cost, with inefficiency arising from unexploited correlations between the measured system and memories, and/or between memories and environment (noise). Using this efficiency, we benchmark two limiting measurement paradigms: sequential, in which the same memory is exploited iteratively, and parallel, in which many memories are exploited simultaneously. In both cases, the minimal erasure cost reflects correlations across memories: temporal in sequential, spatial in parallel. Remarkably, when all system-memory correlations are exploited for inference, both paradigms attain the same minimal erasure cost, even in the presence of noise. Conversely, the parallel paradigm performs better in the presence of unexploited correlations, stemming from hidden memories' degrees of freedom. This approach provides a quantitative, physically grounded criterion to compare inference strategies, determine their efficiency, and link target information gains to their minimal entropic cost.
Quantum state tomography is fundamental to quantum computing verification and quantum cryptography validation, yet existing methods provide point estimates without quantifying when additional measurements are needed. We introduce Latent Posterior Factors (LPF) \citep{aliyu2026lpf,aliyu2026theory}, the first multi-evidence aggregation system with exact uncertainty decomposition for quantum measurements. LPF achieves 99.8% classification accuracy and 0.979 ± 0.051 fidelity on single-qubit tomography, with 50% fewer errors than maximum likelihood estimation (MLE) (0.21% vs. 0.43% error rate) despite MLE's asymptotic optimality. Critically, LPF provides perfectly calibrated uncertainties (Expected Calibration Error 0.17%) and exact epistemic-aleatoric decomposition: 46% of uncertainty is reducible through additional measurements, while 54% represents irreducible quantum randomness. When LPF reports 95% confidence, it is correct 95.1% of the time—enabling experimentalists to make trustworthy decisions about measurement sufficiency. The framework's learned aggregation captures Pauli measurement correlations that violate MLE's independence assumptions, explaining LPF's superior error rate despite lower continuous fidelity metrics. Cross-seed analysis across 11 random initializations demonstrates exceptional robustness (fidelity σ = 0.0003), validating theoretical soundness. Epistemic uncertainty reliably indicates measurement insufficiency, enabling adaptive protocols that achieve 10% measurement reduction in controlled experiments while maintaining accuracy—with production deployments estimated to realize greater savings when accounting for inter-measurement overhead. Keywords:Quantum state tomography, quantum computing verification, uncertainty quantification, epistemic uncertainty, aleatoric uncertainty, uncertainty decomposition, probabilistic inference, multi-evidence aggregation, Latent Posterior Factors (LPF), measurement optimization, maximum likelihood estimation (MLE), calibration (ECE), quantum measurement, adaptive protocols, interpretable uncertainty, quantum information processing, experimental physics AI
Quantum state tomography is fundamental to quantum computing verification and quantum cryptography validation, yet existing methods provide point estimates without quantifying when additional measurements are needed. We introduce Latent Posterior Factors (LPF) \citep{aliyu2026lpf,aliyu2026theory}, the first multi-evidence aggregation system with exact uncertainty decomposition for quantum measurements. LPF achieves 99.8% classification accuracy and 0.979 ± 0.051 fidelity on single-qubit tomography, with 50% fewer errors than maximum likelihood estimation (MLE) (0.21% vs. 0.43% error rate) despite MLE's asymptotic optimality. Critically, LPF provides perfectly calibrated uncertainties (Expected Calibration Error 0.17%) and exact epistemic-aleatoric decomposition: 46% of uncertainty is reducible through additional measurements, while 54% represents irreducible quantum randomness. When LPF reports 95% confidence, it is correct 95.1% of the time—enabling experimentalists to make trustworthy decisions about measurement sufficiency. The framework's learned aggregation captures Pauli measurement correlations that violate MLE's independence assumptions, explaining LPF's superior error rate despite lower continuous fidelity metrics. Cross-seed analysis across 11 random initializations demonstrates exceptional robustness (fidelity σ = 0.0003), validating theoretical soundness. Epistemic uncertainty reliably indicates measurement insufficiency, enabling adaptive protocols that achieve 10% measurement reduction in controlled experiments while maintaining accuracy—with production deployments estimated to realize greater savings when accounting for inter-measurement overhead. Keywords:Quantum state tomography, quantum computing verification, uncertainty quantification, epistemic uncertainty, aleatoric uncertainty, uncertainty decomposition, probabilistic inference, multi-evidence aggregation, Latent Posterior Factors (LPF), measurement optimization, maximum likelihood estimation (MLE), calibration (ECE), quantum measurement, adaptive protocols, interpretable uncertainty, quantum information processing, experimental physics AI