Fundamental limits on concentrating and preserving tensorized quantum resources

TL;DR

This paper establishes fundamental limits on how quantum resources with tensorization properties can be concentrated and preserved under noise, revealing inherent restrictions in quantum resource manipulation.

Contribution

It proves that certain quantum resources cannot be concentrated or better protected from noise using free operations or correlated inputs, given their tensorization and monotonicity properties.

Findings

No concentration of multiple noisy copies into a single improved resource.

Correlated inputs do not enhance protection against channel noise for tensorized resources.

Theorems apply to practical quantum resource measures, clarifying physical limitations.

Abstract

Quantum technology offers great advantages in many applications by exploiting quantum resources like nonclassicality, coherence, and entanglement. In practice, an environmental noise unavoidably affects a quantum system and it is thus an important issue to protect quantum resources from noise. In this work, we investigate the manipulation of quantum resources possessing the so-called tensorization property and identify the fundamental limitations on concentrating and preserving those quantum resources. We show that if a resource measure satisfies the tensorization property as well as the monotonicity, it is impossible to concentrate multiple noisy copies into a single better resource by free operations. Furthermore, we show that quantum resources cannot be better protected from channel noises by employing correlated input states on joint channels if the channel output resource exhibits the tensorization property. We address several practical resource measures where our theorems apply and manifest their physical meanings in quantum resource manipulation.