Fundamental limitations on quantum channel manipulation

Bartosz Regula, Ryuji Takagi

Published 2020-10-22Version 1

We establish universal limitations on the manipulation of quantum channel resources under the most general, adaptive transformation protocols. Focusing in particular on the class of distillation tasks -- which can be understood either as the purification of noisy channels into unitary ones, or the extraction of state-based resources from channels -- we develop fundamental restrictions on the error necessarily incurred in such transformations, applicable to many different settings in general resource theories. We introduce comprehensive lower bounds for the overhead of any physical distillation protocol in terms of required channel uses, imposing strong limitations on the practical efficiency and cost of channel manipulation protocols. In the asymptotic setting, our results yield broadly applicable strong converse bounds for the rates of distillation. As a special case, our methods apply to the manipulation of quantum states, in which case they significantly improve on and extend the recent no-go theorems for resource purification in [Fang and Liu, Phys. Rev. Lett. 125, 060405 (2020)]. We demonstrate our results through explicit applications to quantum communication, where we recover in particular a number of strong converse bounds for the quantum capacity of channels assisted by various classes of operations, as well as to stabilizer quantum computation, where we study the precise quantitative links between magic state distillation and quantum gate synthesis, and provide improved bounds for both tasks.