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A quantum system put in interaction with another one that is repeatedlymeasured is subject to a non-unitary dynamics, through which it is possible toextract subspaces. This key idea has been exploited to propose schemes aimed atthe generation of pure quantum states (purification). All such schemes have sofar been considered in the ideal situations of isolated systems. In this paper,we analyze the influence of non-negligible interactions with environment duringthe extraction process, with the scope of investigating the possibility ofpurifying the state of a system in spite of the sources of dissipation. Ageneral framework is presented and a paradigmatic example consisting of twointeracting spins immersed in a bosonic bath is studied. The effectiveness ofthe purification scheme is discussed in terms of purity for different values ofthe relevant parameters and in connection with the bath temperature.

Influence of dissipation on the extraction of quantum states via repeated measurements