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arXiv:2010.11822 · PRX Quantum

No-Go Theorems for Quantum Resource Purification: New Approach and Channel Theory

Kun Fang, Zi-Wen Liu

Published Mar 8, 2022• 39 citations
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Abstract

A universal and powerful method for analyzing the fundamental limitations on quantum resource purification is presented, enabling a robust no-purification theory for dynamical quantum resources and wide-ranging applications for practical quantum information processing
DOI
10.1103/prxquantum.3.010337

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Measurement incompatibility is a fundamental quantum resource that enables advantages in many quantum information tasks, including cryptography and communication. However, unavoidable interactions between a system and its environment can degrade or even completely destroy measurement incompatibility; such a process is referred to as a measurement-incompatibility-annihilating channel. Recently, the capability of noisy quantum dynamics to preserve measurement incompatibility has been characterized within the resource theory of measurement incompatibility preservability. This motivates studying how to purify the preservation of measurement incompatibility and how to activate it from a measurement-incompatibility-annihilating channel. To this end, we first introduce our figures of merit as robustness-based resource monotones within this resource theory. We demonstrate that while pre-filtering operations can strengthen measurement incompatibility preservability, they cannot activate it from an incompatibility-annihilating channel, establishing a no-go theorem. Furthermore, we explicitly demonstrate that an incompatibility-annihilating channel can be stochastically activated via post-filtering operations. Our results provide a practical framework for exploiting measurement incompatibility in quantum information processing.
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