Singlet-Like Correlations: Equal Peak Work, Unequal Robustness

Abstract

Initial system-environment correlations are a thermodynamic resource, enabling work extraction through their erasure. We compare three representative singlet-like, rotationally covariant correlation laws -- a local classical benchmark, the quantum cosine law, and an idealized stronger-than-quantum step law -- under measurement misalignment. In the binary-outcome, uniform-marginal setting, all three can attain the same peak extractable work, k_{\mathrm B}T\ln 2. Their operational value differs, however, in robustness away from perfect alignment. For the chosen classical benchmark the mutual information degrades as Θ(δθ\ln(1/δθ)), whereas for the quantum cosine law it degrades as Θ(δθ^2\ln(1/δθ)). The stronger-than-quantum step law is perfectly flat except at a critical angle. Accordingly, the paper establishes a robustness hierarchy within this restricted comparison class, rather than a no-go theorem for all classical correlations.