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, kBTln2. Their operational value differs, however, in robustness away from perfect alignment. For the chosen classical benchmark, the mutual information degrades as Θ(δθln(1/δθ)), whereas for the quantum cosine law it degrades as Θ(δθ2ln(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.