Quantum metrology, which studies parameter estimation in quantum systems, has many important applications in science and technology, ranging from frequency spectroscopy to gravitational wave detection. Quantum mechanics imposes a fundamental limit on the estimation precision, called the Heisenberg limit, which is achievable in noiseless quantum systems, but is in general not for noisy systems. This talk is a summary of some recent works by the speaker and collaborators on quantum metrology enhanced by quantum error correction. Specifically, we present a necessary and sufficient condition for achieving the Heisenberg limit in noisy quantum systems. When the condition is satisfied, the Heisenberg limit is recovered by a quantum error correction protocol which corrects all noises while maintaining the signal; when it is violated, we show the estimation limit still in general has a constant factor improvement over classical strategies, and is achievable using approximate quantum error correction. Both error correction protocols can be optimized using semidefinite programs. Examples in some typical noisy systems will be provided.

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