Shortcut-error signatures in coherence-retaining endpoint work quasistatistics

TL;DR

This paper investigates how coherence-retaining quasistatistics can serve as sensitive diagnostics for nonadiabaticity in quantum shortcuts, revealing linear versus quadratic effects of control errors.

Contribution

It introduces a phase-sensitive endpoint diagnostic method that detects residual nonadiabaticity through coherence-retaining quasistatistics, contrasting with traditional TPM results.

Findings

Imperfect shortcuts produce off-diagonal Hamiltonian elements at first order in error amplitude.

Population transition probabilities change only at second order in control errors.

Harmonic oscillator and qubit benchmarks confirm the linear versus quadratic contrast.

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.