Fluctuations of work cost in optimal generation of correlations

We study the impact of work cost fluctuations on optimal protocols for the creation of correlations in quantum systems. We analyze several notions of work fluctuations to show that even in the simplest case of two free qubits, protocols that are optimal in their work cost (such as the one developed by Huber et al. [NJP 17, 065008 (2015)]) suffer work cost fluctuations that can be much larger than the work cost. We discuss the implications of this fact in the application of such protocols and suggest that, depending on the implementation, protocols that are sub-optimal in their work cost could beat optimal protocols in some scenarios. This highlights the importance of assessing the dynamics of work fluctuations in quantum thermodynamic protocols.