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No-Go Theorems for Universal Quantum State Purification via Classically Simulable Operations
Keming He1, Chengkai Zhu1, Hongshun Yao1
1The Hong Kong University of Science and Technology (Guangzhou), Thrust of Artificial Intelligence, Information Hub, Guangdong 511453, China.
Physical Review Letters
|March 20, 2026
Summary
Classically simulable operations cannot universally purify quantum states, even with multiple copies. Nonstabilizer resources are essential for robust quantum information processing and error correction.
Area of Science:
- Quantum Information Science
- Quantum Computing
- Quantum Error Correction
Background:
- Quantum state purification is vital for restoring noisy quantum states in quantum information processing.
- Fault-tolerant quantum computation uses stabilizer operations, which are classically simulable but computationally limited.
Purpose of the Study:
- To investigate the limitations of classically simulable operations for quantum state purification.
- To determine if universal purification is achievable using only these limited operations.
Main Methods:
- Analysis of deterministic and probabilistic purification protocols.
- Application of semidefinite programming and numerical evidence.
- Investigation of qubit systems and systems of odd dimensions.
Main Results:
- Classically simulable operations can enhance fidelity for specific states but cannot achieve universal purification.
- Universal two-to-one purification is impossible using only classically simulable operations for qubits and odd-dimensional systems.
- This limitation extends to using three and four copies of the quantum state.
Conclusions:
- Nonstabilizer resources are indispensable for universal quantum state purification.
- Classically simulable operations have inherent limitations in quantum state purification.
- Full quantum operations are necessary for robust quantum information processing.
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