Entanglement Entropy Is Not a Faithful Explanation: Auditing a Financial Quantum Feature Map
Abstract
Abstract—Entanglement entropy is an attractive candidate for
explaining quantum machine-learning models: it is intrinsic to
the encoding, cheap to compute, and requires no measurement.
We test whether it is a faithful feature attribution for a financialtransaction
quantum feature map, under a protocol predeclared
down to its thresholds, its comparison family, and its posture on
failure. Two questions are separated by construction. First, does
the operating point selected for accuracy leave usable attribution
signal? Second, does that signal correspond to what actually
drives the model’s decisions? On the Kaggle Credit-Card Fraud
dataset over ten repeated case-control splits, per-feature entropy
dispersion is 71% lower at the accuracy-selected entanglement
strength than at the midpoint of the grid, and the difference is
significant after Holm–Bonferroni correction; however, a lowerstrength
regime with 3.4× the dispersion is available at no
statistically detectable accuracy cost. Faithfulness fails decisively.
Entropy rankings are significantly anti-correlated with modelaware
occlusion attributions (median Spearman −0.299), and
on a synthetic task whose informative features are known
by construction and which the quantum model demonstrably
learns, occlusion recovers ground truth (+0.237) while entropy
does not (−0.025), both significant after correction. A modelrandomisation
check identifies the cause exactly: per-feature
entropy is invariant to the trained model, with maximum change
of exactly zero across all ten seeds, so it cannot distinguish a
correctly trained model from one fitted to shuffled labels. We
conclude that entanglement entropy is a genuine and inexpensive
diagnostic of the encoding but not an explanation of the
model, and we report this refutation as predeclared. Balancedcohort
metrics are benchmark values, not deployment-prevalence
estimates.
Keywords—Quantum Machine Learning; Explainable AI; Feature
Attribution; Entanglement Entropy; Quantum Kernel Methods;
Financial Fraud Detection; Negative Results
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