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Quantum technology offers great advantages in many applications by exploitingquantum resources like nonclassicality, coherence, and entanglement. Inpractice, an environmental noise unavoidably affects a quantum system and it isthus an important issue to protect quantum resources from noise. In this work,we investigate the manipulation of quantum resources possessing the so-calledtensorization property and identify the fundamental limitations onconcentrating and preserving those quantum resources. We show that if aresource measure satisfies the tensorization property as well as themonotonicity, it is impossible to concentrate multiple noisy copies into asingle better resource by free operations. Furthermore, we show that quantumresources cannot be better protected from channel noises by employingcorrelated input states on joint channels if the channel output resourceexhibits the tensorization property. We address several practical resourcemeasures where our theorems apply and manifest their physical meanings inquantum resource manipulation.

Fundamental limits on concentrating and preserving tensorized quantum resources