  Although nonequilibrium work and fluctuation relations have been studied in
detail within classical statistical physics, extending these results to open
quantum systems has proven to be conceptually difficult. For systems that
undergo decoherence but not dissipation, we argue that it is natural to define
quantum work exactly as for isolated quantum systems, using the two-point
measurement protocol. Complementing previous theoretical analysis using quantum
channels, we show that the nonequilibrium work relation remains valid in this
situation, and we test this assertion experimentally using a system engineered
from an optically trapped ion. Our experimental results reveal the work
relation's validity over a variety of driving speeds, decoherence rates, and
effective temperatures and represent the first confirmation of the work
relation for non-unitary dynamics.
