Observing quantum work by Margenau-Hill quasiprobability

¹ Department of Physics, Pusan National University - Busan 46241, Korea
² Department of Physics, Korea Advanced Institute of Science and Technology - Deajeon 34141, Korea

Received: 20 February 2025
Accepted: 14 April 2025

Abstract

We consider Margenau-Hill quasiprobability that measures a statistical weight assigned to an observation of an energy eigenvalue pair and its utilization in assessing work done by isolated quantum ensembles that generally contain coherence. We point out some physically reasonable and intuitive features of the statistical properties of work determined by Margenau-Hill quasiprobability. To be specific, we show that in sharp contrast to other proposals, the moment-generating function given by Margenau-Hill quasiprobability fulfills the composition and shift properties, and thus guarantees the additivity of works performed by joined work protocols. Work fluctuations accessed by Margenau-Hill distribution also give expected values for initially pure energy ensembles, providing a rationale as to why it serves as a unique measure in characterizing quantum work and its fluctuations.