Achieving the Heisenberg Limit in Quantum Metrology Using Quantum Error Correction*

Quantum metrology concerns the task of estimating physical parameters describing the Hamiltonian of a quantum system, with wide applications in science and technology. The Heisenberg limit characterizes the fundamental limit of estimation precision for a noiseless quantum system. In practice, however, noise usually imposes a severe limitation on precision, making the Heisenberg limit unachievable. Quantum error correction has been proposed to address this problem in several scenarios, but its potential value in metrology has not yet been fully identified. We present a necessary and sufficient condition for achieving the Heisenberg limit in quantum probes subject to Markovian noise, assuming access to noiseless ancillas and fast and accurate quantum controls. Under such condition, we provide a general construction of quantum error correction codes to recover a noiseless channel without completely eliminating the signal Hamiltonian. Our work opens up a new possibility to achieve the ultimate precision limit in noisy quantum systems. The full paper is available at arXiv:1706.02445.