Środowiskowe Seminarium z Informacji i Technologii Kwantowych

In this contribution we consider the problem of minimizing theancillary systems required to realize an arbitrary strategy of aquantum protocol, with the assistance of classical memory. For thispurpose we introduce the notion of memory cost of a strategy, whichmeasures the resources required in terms of ancillary dimension. Weprovide a condition for the cost to be equal to a given value, and weuse this result to evaluate the cost in some special cases. As anexample we show that any covariant protocol for the cloning of aunitary transformation requires at most one ancillary qubit. We alsoprove that the memory cost has to be determined globally, and cannotbe calculated by optimizing the resources independently at each stepof the strategy.