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We characterize the impact that the application of two maps in aquantum-controlled order has on the process of work extraction via unitarycycles and its optimization. The control is based on the quantum switch modelthat applies maps in an order not necessarily compatible with the underlyingcausal structure and, in principle, can be implemented experimentally. First,we show that the activation of quantum maps through the quantum switch modelalways entails a non-negative gain in ergotropy compared to their consecutiveapplication. We also establish a condition that the maps should fulfill inorder to achieve a non-zero ergotropic gain. We then perform a thoroughanalysis of maps applied to a two-level system and provide general conditionsfor achieving a positive gain on the incoherent part of ergotropy. Our resultsare illustrated with several examples and applied to qubit and $d$-dimensionalquantum systems. In particular, we demonstrate that a non-zero work can beextracted from a system thermalized by two coherently controlled reservoirs.

Work extraction from coherently activated maps via quantum switch