Power and Limitations of Distributed Quantum State Purification

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Abstract
Quantum state purification protocols, which mitigate noise by converting multiple copies of noisy quantum states into fewer copies with a lower noise level, have applications in quantum communication and computation with imperfect devices. Here, we systematically study the task of state purification in distributed quantum systems, demanding that purification be achieved by local operations and classical communication (LOCC). We prove that, in the presence of depolarizing noise, no LOCC purification protocol starting from two copies can work blindly for all the states in three important sets: the set of all pure two-qubit states, the set of all two-qubit maximally entangled states, and the Bell basis. In stark contrast, we show that a targeted, single-state purification is always achievable in the presence of depolarizing noise, and we provide an explicit analytical LOCC protocol for every given two-qubit state. For arbitrary finite sets of pure states and arbitrary noise profiles, we develop an optimization-based algorithm that systematically designs LOCC purification protocols, and we demonstrate it through concrete examples. Overall, our results identify both fundamental limitations and practical noise-reduction strategies for distributed quantum information processing.
Funding Information
  • Ministry of Science and Technology of the People's Republic of China (2023ZD0300600)
  • Chinese University of Hong Kong
  • National Natural Science Foundation of China (12447107)
  • Natural Science Foundation of Guangdong Province (2025A1515012834)
  • Hong Kong Research Grant Council (R7035-21F)
  • State Key Laboratory of Quantum Information Technologies and Materials
  • Guangdong Provincial Quantum Science Strategic Initiative (GDZX2403008)
  • Guangdong Provincial Quantum Science Strategic Initiative (GDZX2503001)
  • Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area

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