  Work is a process-based quantity, and its measurement typically requires
interaction with a measuring device multiple times. While classical systems
allow for non-invasive and accurate measurements, quantum systems present
unique challenges due to the influence of the measuring device on the final
value of work. As recent studies have shown, among these challenges is the
impossibility of formulating a universal definition of work that respects
energy conservation for coherent quantum systems and is compatible with the
Jarzynski equality - a fluctuation relation linking the equilibrium free energy
difference to the non-equilibrium work. Here we overcome this challenge by
introducing a genuinely quantum, positive correction to the Jarzynski equality
stemming from imposing energy conservation. When sufficiently large, this
correction forces quantum work to violate the second law more often. Moreover,
we construct modified two-point measurement (TPM) schemes for work that ensure
energy conservation for coherent quantum states and align with our
quantum-corrected fluctuation relation. We further underscore the practicality
and effectiveness of these schemes by providing detailed circuit
implementations for them.
