  We consider continuously monitored quantum systems and introduce definitions
of work and heat along individual quantum trajectories that are valid for
coherent superpositions of energy eigenstates. We use these quantities to
extend the first and second laws of stochastic thermodynamics to the quantum
domain. We illustrate our results with the case of a weakly measured driven
two-level system and show how to distinguish between quantum work and heat
contributions. We finally employ quantum feedback control to suppress detector
backaction and determine the work statistics.
