  We consider measurement based single temperature quantum heat engine without
feedback control, introduced recently by Yi, Talkner and Kim [Phys. Rev. E 96,
022108 (2017)]. Taking the working medium of the engine to be a one-dimensional
Heisenberg model of two spins, we calculate the efficiency of the engine
undergoing a cyclic process. Starting with two spin-1/2 particles, we
investigate the scenario of higher spins also. We show that, for this model of
coupled working medium, efficiency can be higher than that of an uncoupled one.
However, the relationship between the coupling constant and the efficiency of
the engine is rather involved. We find that in the higher spin scenario
efficiency can sometimes be negative (this means work has to be done to run the
engine cycle) for certain range of coupling constants, in contrast to the
aforesaid work of Yi, Talkner and Kim, where they showed that the extracted
work is always positive in the absence of coupling. We provide arguments for
this negative efficiency in higher spin scenarios. Interestingly, this happens
only in the asymmetric scenarios, where the two spins are different. Given
these facts, for judiciously chosen conditions, an engine with coupled working
medium gives advantage for the efficiency over the uncoupled one.
