Shortcut-error signatures in coherence-retaining endpoint work quasistatistics

Abstract

Quantum work statistics differ from classical ones because initial energy coherence matters. The standard two-point measurement (TPM) gives a positive distribution but erases phase information. Coherence-retaining endpoint-work quasistatistics provide a compact probe of shortcut-to-adiabaticity performance. For work defined with respect to a reference Hamiltonian, an exact counterdiabatic shortcut pulls the final reference Hamiltonian back to an operator diagonal in the initial energy basis. Endpoint Kirkwood-Dirac or Margenau-Hill quasistatistics then lose sensitivity to initial coherence and reduce to the TPM result. Imperfect shortcuts restore this sensitivity: a non-commuting control error produces off-diagonal pulled-back Hamiltonian elements at first order in the error amplitude, whereas population-only transition probabilities change only at second order. Harmonic-oscillator and qubit benchmarks confirm this linear-versus-quadratic contrast. The result complements inclusive work-cost analyses: it does not measure the auxiliary field's energetic cost, but provides a phase-sensitive endpoint diagnostic of residual nonadiabaticity.