Quasi-probability distribution of work in a measurement-based quantum Otto engine

We study the work statistics of a measurement-based quantum Otto engine, where quantum non-selective measurements are used to fuel the engine, in a coupled spin working system (WS). The WS exhibits quantum coherence in the energy eigenbasis at the beginning of a unitary work extraction stage in presence of inter-spin anisotropic interaction. We demonstrate that the probability of certain values of stochastic work can be negative, rendering itself akin to the quasi-probability distribution found in phase space. This can be attributed to the interference terms facilitated by quantum coherence. Additionally, we establish that coherence can improve the average work in finite time. Subsequently, we compare the work distribution with a standard QOE operating between two heat baths. We find that, because of the absence of quantum coherence, the probability of stochastic work cannot be negative in a standard QOE.